21 votes
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Intuition behind the differential equation for forced oscillations

It's better to write the differential equation for forced oscillations in a different way that makes it more relatable to Newton's second law: $$m\ddot{x}=F_0\sin{(\omega''t)}-b\dot{x}-kx$$ Now we can ...
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11 votes
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Why is Dirac's Phase Operator Non-Hermitian?

Yeah, that's a strange thing to say - indeed $an^{-1}a^\dagger$ is defined everywhere and equal to the identity (note that $n^{-1}$ itself is not defined everywhere - but it is defined on the image of ...
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6 votes

Why is Dirac's Phase Operator Non-Hermitian?

I'd do it the other way round: $$ (e^{i\phi})^\dagger e^{i\phi} $$ should also be the identity, but $$ (e^{i\phi})^\dagger e^{i\phi}= n^{-1/2} a^\dagger a n^{-1/2} $$ is not defined on $|0\rangle$ as ...
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6 votes

Why is Dirac's Phase Operator Non-Hermitian?

We have in fact to check whether for $U:=\exp i\hat \phi$ it holds that $$UU^\dagger = \mathbb I = U^\dagger U \quad . $$ In Phase and Angle Variables in Quantum Mechanics (where in section 5 it is ...
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4 votes
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Probability of observing harmonic oscillator at a particular position

When dealing with continuous distributions, one should make difference between probability and probability density. Probability of hitting any specific point of a continuous distribution is zero, ...
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