This is a question about simple non-relativistic quantum mechanics in one dimension.(adsbygoogle = window.adsbygoogle || []).push({});

If the energy operator is [tex]\imath \frac{h}{2\pi}\frac{\partial}{\partial t}[/tex], then it would appear to commute with the position operator [tex]x[/tex]. Then, if the energy and position operators commute, I ought to be able to find simultaneous eigenstates of them.

However, it is clear that in general the Hamiltonian does not commute with [tex]x[/tex], and in general these two operators do not have any simultaneous eigenstates.

What is wrong with my thinking? Does it make sense to think of [tex]\imath \frac{h}{2\pi} \frac{\partial}{\partial t}[/tex] as the energy operator, and is that supposed to be the same as the Hamiltonian? Am I running into a problem because I am thinking on the one hand of a time-independent problem and on the other of a time-dependent one? Alternatively, is it incorrect to state that any two operators which commute must have simultaneous eigenstates?

Thank you,

Mark

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# Commutator of Position and Energy

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