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Myth 1 is discussed here:

https://www.physicsforums.com/showthread.php?t=229497

The myth 1 thread is still alive but, personally, I would like to press on. I will be offline for most of the month of June and want to get through all these, if possible.

**In QM, there is a time-energy uncertainty relation**

The topic is the claim that the common statement that time and energy are related by an uncertainty relation similar to that for position and momentum is a myth. By myths we mean widely repeated statements which, true or false, are not something we can validly assert given our current understanding.

I have a preliminary question. I have seen the statement that the energy operator is the hamiltonian and not [tex]i\hbar \frac{\partial}{\partial t}[/tex]. That is not how I would put it, though I am quite ready to admit I know little about it. But I would have supposed that [tex]i\hbar \frac{\partial}{\partial t}[/tex] really is the energy operator [tex]E[/tex] and that the condition

[tex]H|\psi\rangle = i\hbar \frac{\partial}{\partial t}|\psi\rangle [/tex]

is a constraint of sorts, telling us a relation between the energy and the other variables which physical systems must satisfy.

Could someone else elaborate on the relationship between E and H?