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## Summary:

- I'm having trouble, or at least am unsure of my interpretation of stationary states and standard deviations of dynamical observables.

## Main Question or Discussion Point

I am currently reading Griffiths Introduction to Quantum Mechanics, 2nd Edition. I am aware that, in light of considering potential functions independent of time, the Schrödinger equation has separable solutions and that these solutions are stationary states. I am also aware (If I stand correct) that the stationary states can be put into a linear combination (I'm supposing for now states without the time dependent solution attached, which is the exponential factor obtained from the method of separation of variables) to form a wave function that is also a solution to the time independent SE.

1) Am I correct in interpreting each term of the linear combination (without the time dependence) as a single stationary state of the wave function? Is this still true if we tack on the time dependence?

2) For stationary states, the standard deviation of the Hamiltonian is zero (I believe). However, my state of confusion arised in doing a problem where the standard deviation of the Hamiltonian was NOT zero. Why is this the case?

I would appreciate any help or guidance in putting me on the right track, if it seems that my train of thought is derailing in any manner.

1) Am I correct in interpreting each term of the linear combination (without the time dependence) as a single stationary state of the wave function? Is this still true if we tack on the time dependence?

2) For stationary states, the standard deviation of the Hamiltonian is zero (I believe). However, my state of confusion arised in doing a problem where the standard deviation of the Hamiltonian was NOT zero. Why is this the case?

I would appreciate any help or guidance in putting me on the right track, if it seems that my train of thought is derailing in any manner.

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