All Questions
Tagged with probability quantum-mechanics
822 questions
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Is the momentum wave function's square amplitude always time-invariant for a free particle? [closed]
I have noticed whenever working with free particles that the square amplitude of the momentum wave function $|\Phi(p)|^2$ ends up being time invariant, so I followed this chain of logic supporting the ...
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1
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How can a quantum particle in an infinite potential well transition between regions separated by nodes? [duplicate]
I don't understand, if the PD describes the probability of finding the particle at a point, how is the probability is non-zero after a node. That means (classically speaking) the particle will have to ...
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0
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61
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Physical interpretation of the matrix element
In perturbation theory, but also in other scenarios the claim is made that the following expression:
$|\langle f|\hat O||i\rangle|^2$ represents the probability amplitude for a transition of the ...
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4
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2
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"Probability of finding a system in a given state" in rigorous quantum mechanics
Feynman and Hibbs pg. 164 includes this paragraph:
The time development of a quantum-mechanical system can be pictured as follows. At an initial time $t_a$ the state is described by the wave function ...
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68
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Dirac delta function as probability density
In Quantum Physics Gasiorowicz states:
Incidentally, had we allowed for discontinuities in $\psi$(x, t) we would have been led to delta functions in the flux, and hence in the probability density, ...
4
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2
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350
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Could probability amplitude for a path equal a complex number whose length is always 1 and whose angle is the action divided by Planck's constant?
I'm reading "Zee A. - Quantum Field Theory, as Simply as Possible", where near beginning of explanation of QFT he gives what appears to be path integral formulation, he states:
The ...
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1
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2
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Quantum tunneling through step potential: How to calculate transmission coefficient?
In case of a finite potential barrier ($V(x) = V_0$ for $-a<x<a$ and $V(x) = 0$ otherwise). We assume a particle is incident from one side say left and is moving right. In the region $x<-a$; ...
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Proof $| \psi |^2$ is probability density
Let's assume
$$\iiint_{\mathbb{R}^3} | \psi |^2 d^3r=1$$
For some $t=t_0$. Then we want to calculate:
$$\frac{d}{dt}\iiint_{\mathbb{R}^3} | \psi |^2 d^3r=\iiint_{\mathbb{R}^3} \frac{\partial | \psi |^...
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2
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Clarification on when to apply the Born Rule in quantum mechanical measurement problems
One of the postulates of quantum mechanics says that if $A$ is an operator corresponding to some observable, with eigenbasis $\{ |a_i\rangle \}_i$, and we measure some state $|\psi\rangle$ to be in ...
-3
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1
answer
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Uncertainty principle probability [closed]
How are positional probabilities and momentum probabilities determined in the principle of uncertainty?
For example, if the position probability is 30, does it work like the momentum probability is 70....
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Laplace's demon and quantum mechanics paradox of not influencing our world? [duplicate]
We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all ...
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1
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Time dependency of Wave function and its probability density function (PDF) [closed]
When we study the Schrodinger wave equation, we have a time dependent wave function $\Psi(x,t)$, and when we deduce its Probability Density function we come to know there is no time dependence in the ...
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2
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Quantum Mechanical Current Normalisation
Consider an electron leaving a metal. The quantum-mechanical current operator, is given (Landau and Lifshitz, 1974) by
$$
j_x\left[\psi_{\mathrm{f}}\right]=\frac{\hbar i}{2 m}\left(\psi_{\mathrm{f}} \...
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1
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What is the physical meaning of the normalization of the propagator in quantum mechanics?
Suppose we have a quantum field theory (QFT) for a scalar field $\phi$ with vacuum state $|\Omega\rangle$. Then, in units where $\hbar = 1$, we postulate that the vacuum expectation value (VEV) of any ...
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4
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Quantum: Which improbable macroscopic events are possible?
Basically, the title. Web search had not found pages in top results with similar QA.
E.g. I understand nuclear blast can just end at any time because random chain-reaction has probability of not ...
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Probabilistic behavior of quantum mechanics [closed]
In a hypothetical scenario, if I were to measure the quantum spin of an electron and it showed "up," and then I traveled back in time without changing the initial conditions, would measuring ...
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3
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937
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Is the zero vector necessary to do quantum mechanics?
Textbook quantum mechanics describes systems as Hilbert spaces $\mathcal{H}$, states as unit vectors $\psi \in \mathcal{H}$, and observables as operators $O: \mathcal{H} \to \mathcal{H}$. Ultimately, ...
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540
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Physical meaning of each term of the square modulus of a wave function
The expression below is the square modulus of the wave function of a harmonic potential ($V=\frac{1}{2}m\omega^2 x^2$) in which it's stated that the probability of finding the particle in the $\psi_0$ ...
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3
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117
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Boltzmann distributions on atomic orbitals: infinite degeneracy?
The (unnormalized) Boltzmann probability distribution of states as a function of energy and temperature is given by
$$P(\epsilon_i) \propto g_i\exp\left(\frac{-\epsilon_i}{k_BT}\right)$$
with $P(\...
1
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0
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Fermi's Golden Rule: Interpreting the Dirac Delta in Transition Probabilities [duplicate]
I am trying to understand an aspect of Fermi's golden rule in the case of a constant perturbation, $V$. The formula for the transition probability from an initial state $i$ to a final state $f$ is ...
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6
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How are quantum systems different from dice?
I've had this question for a while:
Is a state space $\mathcal{H}$ for a quantum system just a sample space in a probability space?
The question arises because i can't really tell a difference between ...
0
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1
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105
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Equation for probability of quantum tunneling
I am looking at fusion reactions in stars and came across how particles will bypass the Coulomb barrier through quantum tunneling. I was wondering if there is an equation for the probability of a ...
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How are uncertainties of the quantum state/wavefunctions themselves modeled?
This question might be confusing so let me try to clarify this carefully.
The wavefunction is a tool that allows us to calculate probability distributions that model uncertainties. Thus makes sense.
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3
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Why a probability distribution in RHS in deriving Bell's Inequality?
Why is there typically an integral over a probability distribution in the RHS of a derivation of Bell's inequality
$$|P(\boldsymbol{a}, \boldsymbol{b}) - P(\boldsymbol{a}, \boldsymbol{c})| \leq \int{p(...
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The role of probability in the many-worlds interpretation [duplicate]
A quantum system can transition to one of two states, with probabilities 30% and 70%. The many worlds interpretation says that the universe splits into two, one for each state. If so, what do the 30% ...
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How is the inner product of two quantum states related to their associated Bloch vectors?
I have a doubt about how two equivalent ways of calculating the inner product between two states seem to not be actually equivalent, as they should. In particular, I'm interested in the case where the ...
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1
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34
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A question about time evolution of position distributions
If I have two probability distributions $P$ at $t$ and $P’$ at $t’$ separated by some time interval. Then, can I describe the transform between the two distributions as $$P’(x) = \int P(a) D(a, x-a, t’...
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Interpretation of nodes of infinite square well [duplicate]
In the infinite square well, there is zero probability of finding a particle at nodes. What is the meaning of this result? Does the particle teleport in the regions between the nodes?
Or is it that ...
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1
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Why do the Schrödinger and Dirac equations contain the mass?
I know the Schrödinger equation is bascially the "quantized" Hamiltonian formalism from classical mechanics, and the Dirac equation is the special-relativistic version. But these equations ...
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Where is my mistake in using a measurement operator instead of Born’s rule to calculate the probability of detecting photons at an arbitrary angle?
As I asked in this question: https://quantumcomputing.stackexchange.com/questions/36998/how-can-i-calculate-the-measuring-probabilities-of-a-two-qubit-state-along-a-cer/37000#37000
From here I know ...
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Infinite potential well suddenly expanding
Problem statement: an electron is in its fundamental state in an infinite (1-dimensional) potential well, its walls being located at $x=0$ and $x=a$. Suddenly, the right wall moves from $x=a$ to $x=2a$...
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Momentum probability density and its normalization
Let the (normalized) wave function $\Psi(x,y)$ represent a free particle in the XY plane. I know $|\Psi|^2$ gives me the probability density function of the particle's position, which I can then ...
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3
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Relation between classical probability and quantum probability formulae
Assuming superposition state
$$
\Psi = C_1 \psi_1 + C_2 \psi_2
$$
,one can write the expectation value $\langle A \rangle$ of a physical magnitude A as follows
$$
\langle A\rangle = P_1 \langle A\...
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Uncertainty principle for incompatible observables whose probability distributions lack well-defined moments
The Heisenberg uncertainty principle states that the product of standard deviations (or variances) for incompatible observables has a non-zero lower bound (with a zero lower bound reserved for ...
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Axiomatic Treatment of Quantum Probability Theory
Define quantum probability theory to be an axiomatic mathematical theory which appropriately generalizes classical (Kolmogorov) probability theory to provide the precise probabilistic framework ...
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1
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Measurement of electrons positions in an orbital, thought experiment
An orbital can hold upto 2 electrons. Let's take 1s orbital of helium.
Now, we use probability density to depict where we can find the electrons in the orbital if we make measurements. Since two ...
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Continuum bases: why do we use dirac delta function? [duplicate]
In discrete bais, we can express a vector as
$$ |\psi\rangle=\sum_{i} c_i|e_i\rangle $$
with orthonormality
$$ \langle e_i|e_j\rangle=\delta_{ij}.$$
$\delta_{ij}$ is usual kronecker delta. If we ...
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Why is psi square a possibility? [duplicate]
Is psi square just an assumption? Or there is a physical reason why they defined like that? My procedure is:
It is intuitive for me to think possibility is proportional to energy distribution. ...
김건형
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2
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Is energy only conserved statistically in quantum mechanics?
I know that a system's energy can be measured with an energy that can be below or above the expectation value, if the system was not in an energy eigenstate, so that energy is only conserved on ...
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Can the probability of finding a particle in a certain finite region be zero?
Don't worry this time isn't about doubleslit but I'll still use it for my question.
Imagine an electron is emitted from the source and I shall allow a certain amount of time to lapsed so as to provide ...
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Probability current density of gaussian wavepacket
This was the question that was asked in an exam.
For a gaussian wavepacket $$ \psi(x,t) = Ae^{\frac{x^2}{4a^2}}e^{i(k_0x-\omega_0t)} $$ corresponding to a free particle, (i) Find the probaibility ...
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Why classical probability is insufficient for quantum mechanics
I've started reading Brian Hall's Quantum Mechanics for Mathematicians. He gives a motivation for the operator formalism for quantum mechanics. If you think of position of a particle as a random ...
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Stern-Gerlach experiment and probability theory
I'm trying to understand why, precisely, we cannot use classical probability theory in quantum mechanics. I came across an explanation of the Stern-Gerlach experiment, saying that if $X$ and $Z$ are ...
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Is there a general construction for three-outcome qutrit POVMs?
For qubits, I can consider the General POVM elements: $M_{\pm} = \frac{1}{2}(I \pm \hat{n}\cdot\overline{\sigma})$ where $\sigma $ is a vector containing the Pauli matrices and $\hat{n}$ a vector with ...
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Why are expectation values of an observable important in QM?
I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution ...
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Most probable position of finding an electron represented in cartesian and spherical coordinates
Consider the probability of finding an electron within a region:
$$P= \iiint |\psi(x,y,z)|^2 dxdydz$$
I would think that The probability of finding an electron at a single point in space would be ...
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Equivalence between CGLMP inequality and CHSH inequality
In this paper, they claim that the inequality $$I = P(A_1 = B_1) + P(B_1 = A_2 + 1) + P(A_2 = B_2) + P(B_2 = A_1) \leq 3$$ is equivalent to the CHSH inequality $$|E(A_1,B_1) - E(A_2,B_1) + E(A_2,B_2) +...
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What is a cross section, really? [closed]
Upon looking at different resources, there is a common definition of a cross section (in the context of QFT) to be the probability that some scattering process occurs. For example, here is a ...
user310742
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Dirac's definition of probability in quantum mechanics
I'm currently reading "The principles of quantum mechanics" by Dirac, and I'm having some trouble understanding some of his assumptions, because in the quantum mechanics course I'm following ...
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
I'm working through the book "Introduction to the Theory of Quantum Information Processing" by Bergou and Hillary, and I've encountered a scenario that I'm not sure how to approach. In ...
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