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Introductory Physics Homework Help
Question about QM eigenvalues.
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[QUOTE="Craptola, post: 4529812, member: 357233"] I've been wrestling with this question for a while and can't seem to find anything in my notes that will help me. [h2]Homework Statement [/h2] Determine whether the wave function [itex]\Psi (x,t)= \textrm{exp}(-i(kx+\omega t))[/itex] is an eigenfunction of the operators for total energy and x component of momentum, and if it is, calculate the eigenvalues.[h2]Homework Equations[/h2] Condition for an eigenfunction: [tex]\hat{E}\Psi =k\Psi [/tex] Where K is the eigenvalue Energy operator: [tex]\hat{E}=i\hbar\frac{\partial }{\partial t}[/tex][h2]The Attempt at a Solution[/h2] Determining that psi is an eigenfunction is easy enough. [tex]\hat{E}\Psi =i\hbar\frac{\partial }{\partial t}[\textrm{exp}(-i(kx+\omega t))][/tex] [tex]=-i\hbar i\omega \Psi =\hbar\omega \Psi =\frac{h}{2\pi }2\pi f\Psi =hf\Psi =E\Psi [/tex] I can't figure out how to calculate the value of E from this information alone. I imagine the same method works for momentum when I figure out what it is. [/QUOTE]
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Introductory Physics Homework Help
Question about QM eigenvalues.
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