All Questions
17 questions
4
votes
2
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195
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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 ...
- 860
4
votes
2
answers
350
views
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 ...
- 645
2
votes
1
answer
92
views
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 ...
2
votes
1
answer
122
views
Why must the propagator exponent be imaginary?
In response to asmaier's question, qmechanic showed why the propagator must be $\exp(cS)$. That made perfect sense. But can it also be shown that $c$ is imaginary? I believe it follows from ...
- 21
2
votes
1
answer
156
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Free particle probability to go from $a$ to $b$ [duplicate]
Feynman and Hibbs write that the probability
for a particle to go from $a$ to $b$ is
\begin{equation*}
P(b,a)=|K(b,a)|^2
\end{equation*}
The kernel for a free particle is given as
\begin{equation*}
K(...
- 397
4
votes
2
answers
264
views
Intuitively, why does Quantum Mechanics involve a sum over all possibilities?
I understand that one can just mathematically derive the path integral from the Schrodinger equation. I'm looking for an intuitive explanation in contrast with classical mechanics.
Consider a ...
- 6,768
1
vote
0
answers
75
views
Can this shape of matrix elements in the path integral formalism be linked to some sort of expectation value?
This question is about expressions of the form
$$
\langle x_f, t_i | \hat{x}(t) | x_i, t_i \rangle = \frac{1}{N} \int_{x(t_i) = x_i}^{x(t_f) = x_f} \mathcal{D} x~x(t)e^{i S[x]}.
$$
In the following ...
- 6,980
0
votes
0
answers
49
views
Quantum mechanics propagator as transition amplitude [duplicate]
In QM, the following object:
$$U(x_{f},t_{f}; x_{i},t_{i}) = \langle x_{f},t_{f}|x_{i},t_{i}\rangle$$
is called propagator. Its interpretation is that it is the transition amplitude from a particle to ...
- 1,141
1
vote
1
answer
374
views
Relativity and Quantum Mechanics
I have been thinking about the problem of relativistic path integrals and I encountered several difficulties.
Let's assume we have a particle initially a position $x_i$ at $t_i$ in a certain reference ...
- 1,518
5
votes
3
answers
828
views
Path integral kernel dimensions and normalizing factor
I am currently reading Quantum Mechanics and Path Integrals by Feynman and Hibbs. Working on problem 3.1 made me wonder why the 1D free particle kernel: $$ K_0(b,a) = \sqrt\frac{m}{2\pi i \hbar(t_a - ...
- 51
7
votes
3
answers
701
views
Limit as $x_1 \to x_0$ for the propagator of the harmonic oscillator
Consider a non-relativistic particle of mass $m$, moving along the $x$-axis in a potential $V(x) = m\omega^2x^2/2$. use path-integral methods to find the probability to find the particle between $x_1$ ...
user71299
-2
votes
1
answer
680
views
probability amplitude and path integrals [closed]
Recently, I have been learning about path integrals and I was wondering, can the probability of a certain path be weighted more in a path integral? Said in another way, can certain paths have more ...
- 1,775
8
votes
2
answers
1k
views
Interpretation: probability form probability amplitude (free particle)
If you compute the probability amplitude of a free 1D non-relativistic particle with mass $m$, located at position $x_0$ at time $t_0$, for beeing detected at some other point $x_N$ at time $t_N$ you ...
- 378
18
votes
1
answer
3k
views
Normalizing Propagators (Path Integrals)
In the context of quantum mechanics via path integrals the normalization of the propagator as
$$\left | \int d x K(x,t;x_0,t_0) \right |^2 ~=~ 1\tag{1}$$
is incorrect. But why?
It gives the correct ...
- 944
4
votes
1
answer
801
views
Classical mechanics from Quantum mechanics
I'm looking at a way to prove that one recovers, under ad hoc assumptions, classical mechanics from quantum theory. Usually, we can find in textbooks that the propagator
$$K(x,x_0;t)=\langle x|e^{-i ...
- 12.1k
10
votes
2
answers
4k
views
Normalization of the path integral
When one defines the path integral propagator, there is the need to normalize the propagator (since it would give you a probability density). There are two formulas which are used.
1) Original (v1+v2)...
- 3,132
12
votes
2
answers
1k
views
Question about a Limit of Gaussian Integrals and how it relates to Path Integration (if at all)?
I have come across a limit of Gaussian integrals in the literature and am wondering if this is a well known result.
The background for this problem comes from the composition of Brownian motion and ...
- 223