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land
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One more question. Sorry!
Here's the problem:
An electron moves in a straight line under the influence of a conservative force so that the Hamiltonian is [tex]H = \frac{p\wedge^2}{2m} + V(x)[/tex], where [tex]p\wedge[/tex] means the momentum operator and I think V(x) is the potential energy. I need to find an expression for [tex]\frac{d}{dt} <\frac{p^2}{2m}>[/tex].
Sigh. Anyone have any idea how to do this? I wish I could show you something that I've done to get started but I really don't have a clue. I do have an expression for the time-derivative of an operator.. but plugging this into it involves time derivatives of integrals over x and figuring out the commutator of H and p^2 / 2m, which involves doing calculations with the potential energy, and I have no idea how to deal with that. Thanks.
Here's the problem:
An electron moves in a straight line under the influence of a conservative force so that the Hamiltonian is [tex]H = \frac{p\wedge^2}{2m} + V(x)[/tex], where [tex]p\wedge[/tex] means the momentum operator and I think V(x) is the potential energy. I need to find an expression for [tex]\frac{d}{dt} <\frac{p^2}{2m}>[/tex].
Sigh. Anyone have any idea how to do this? I wish I could show you something that I've done to get started but I really don't have a clue. I do have an expression for the time-derivative of an operator.. but plugging this into it involves time derivatives of integrals over x and figuring out the commutator of H and p^2 / 2m, which involves doing calculations with the potential energy, and I have no idea how to deal with that. Thanks.
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