- #1
Cogswell
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Here's the question:
1. In classical mechanics, we know that the evolution of a system, that is the trajectories of the particles and objects, does not depend on where we chose the xero-point of the potential energy. Here we analyse what happens in quantum mechanics. Assume that you add a constant C0 to the potential energy of an arbitrary potential V(x)
Show that the wave function now differs from the one you would get without the C0 added by having a phase factor [tex]e^{-i \frac{C_0 t}{\hbar}}[/tex] multiplied to it.
How will this phase-factor affect the expectation value of a dynamical variable?
So I was thinking of using: [tex]\Psi (x,t) = \psi (x) \varphi (x)[/tex]
to solve it.
Can someone guide me through this (like with a hint or 2)? I'm quite confused about quantum mechanics.
1. In classical mechanics, we know that the evolution of a system, that is the trajectories of the particles and objects, does not depend on where we chose the xero-point of the potential energy. Here we analyse what happens in quantum mechanics. Assume that you add a constant C0 to the potential energy of an arbitrary potential V(x)
Show that the wave function now differs from the one you would get without the C0 added by having a phase factor [tex]e^{-i \frac{C_0 t}{\hbar}}[/tex] multiplied to it.
How will this phase-factor affect the expectation value of a dynamical variable?
So I was thinking of using: [tex]\Psi (x,t) = \psi (x) \varphi (x)[/tex]
to solve it.
Can someone guide me through this (like with a hint or 2)? I'm quite confused about quantum mechanics.