- #1
Lengalicious
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Homework Statement
See attachment
Homework Equations
The Attempt at a Solution
(i) [tex]|\Psi(t)_{1}>=e^{{-itE_{1}/\hbar}}\frac{1}{\sqrt{2}}(|z^{+}>+|z^{-}>)[/tex]
[tex]|\Psi(t)_{2}>=e^{{-itE_{2}/\hbar}}\frac{1}{\sqrt{2}}(|z^{+}>-|z^{-}>)[/tex]
where [tex]E_{1}=\lambda\frac{\hbar^{2}}{4}+\mu\frac{\hbar}{2}[/tex]
[tex]E_{2}=\lambda\frac{\hbar^{2}}{4}-\mu\frac{\hbar}{2}[/tex]
(ii) [tex]|\Psi(t)>=\sum_{i}c_{i}(0)e^{{-itE_{i}/\hbar}}|\Psi_{i}>[/tex]
(iii) [tex]|<\psi(t)_{2}|\psi(0)_{1}>|^{2}=[/tex]
[tex]|(e^{it(\lambda\hbar^{2}/4-\mu\hbar/2)/\hbar}<z^{-}|)^{*}(|z^{+}>)|^{2}=0[/tex]
I feel like I'm doing something really wrong could someone check over my attempt please and guide me in the right direction if I'm doing it wrong.