New answers tagged harmonic-oscillator
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How to derive this expression for the free scalar field in QFT? (Peskin & Schroeder)
I know that this has already been answered, but I was struggling with this myself, specifically in following Peskin's Argument where he drew an analogy with the quantum harmonic oscillator. I'm ...
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Accepted
Approximation to the differential equation $\dfrac{d^2\psi}{d \xi^2} = \xi^2 \psi$ for large values of $\xi$
Actually, taking
\begin{align}
\frac{d^2}{d\xi^2}\left(A e^{-\xi^2/2} + B e^{\xi^2/2}\right)&= A e^{-\xi^2/2}(\xi^2-1) + B e^{\xi^2/2}(\xi^2+1) \\
& = \xi^2 \left(A e^{-\xi^2/2} + B e^{\xi^2/2}...
- 47.9k
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Why is circular motion "simple harmonic" when there is no restoring force?
I want to make a correction. Uniform circular motion is NOT a simple harmonic motion. It is the projection of uniform circular motion on the diameter of the circular path that is in simple harmonic ...
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What is the partition function of a classical harmonic oscillator?
The $h^{-3}$ is needed to get the correct units, but there is more to it. $h^{-3}$ is the elementary volume of phase space needed for one quantum state. This constant cannot be found by classical ...
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How do you derive the compound pendulum formula?
Here is a rough proof:
Manipulating $\omega=\sqrt{\frac{g}{l}}$ gives
$\begin{align}\frac{2\pi}{T}=\sqrt{\frac{g}{l}}\\T=2\pi\sqrt{\frac{l}{g}}\\=2\pi\sqrt{\frac{ml^2}{mgl}}=2\pi\sqrt{\frac{I}{mgl}}\\\...
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