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latnoa
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Homework Statement
A particle of mass m moves in the potential energy V(x)= [itex]\frac{1}{2}[/itex] mω2x2
. The ground-state wave function is
[itex]\psi[/itex]0(x)=([itex]\frac{a}{π}[/itex])1/4e-ax2/2
and the first excited-state wave function is
[itex]\psi[/itex]1(x)=([itex]\frac{4a^3}{π}[/itex])1/4e-ax2/2
where a = mω/[itex]\hbar[/itex]
What is the average value of the parity for the state
ψ(x)=[itex]\frac{\sqrt{3}}{2}[/itex][itex]\psi[/itex]0(x)+ [itex]\frac{1-i}{2\sqrt{2}}[/itex][itex]\psi[/itex]1(x)
Homework Equations
∏[itex]\psi[/itex](x)=[itex]\psi[/itex](-x)
∏[itex]\psi[/itex]λ(x) = [itex]\psi[/itex]λ(x)
The Attempt at a Solution
First off I'm extremely confused on how to approach this to the point of where I don't know what I'm solving for so I'm someone can help me understand the problem and what it's asking me to do.
I just finished reading the parity operator section and all I understand was that ∏ inverts the coordinates of the wave function. I also got that ∏^2 is the identity vector which means that the eigenvalues have to be ±1 and that an even eigenfunction corresponds to 1 while an odd function corresponds to -1 and The eigenfunction of the parity operator form a complete set. That's it from the book but it shows no examples or anything remotely close to what this questions asks.
Am I trying to solve for ∏? Why are the ground state and first state included in this problem? Please help. Anything will be helpful.
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