1167_Physics ProblemsTechnical Physics

1167_Physics ProblemsTechnical Physics - 508 Quantum...

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508 Quantum Mechanics P41.45 (a) f E h == ×⋅ × F H G I K J 180 6626 10 160 10 434 10 34 19 14 . . . . eV Js J 1.00 eV Hz a f ej (b) λ × × = c f 300 10 691 10 691 8 14 7 . . . ms Hz m n m (c) ∆∆ Et = 2 so E t h t ≥= = × = × −− = 24 4 2 00 10 2 64 10 1 65 10 34 6 29 10 π af . . .. s J e V *P41.46 (a) Taking LLL xy , we see that the expression for E becomes E h mL nn e =+ 2 2 22 8 . For a normalizable wave function describing a particle, neither n x nor n y can be zero. The ground state, corresponding to 1, has an energy of E h h ee 11 2 2 2 2 8 4 , = . The first excited state, corresponding to either n x = 2, n y = 1 or n x = 1, n y = 2 , has an energy EE h h 21 12 2 2 2 2 8 5 8 ,, + = . The second excited state, corresponding to n x = n y = 2 has an energy of E h h 2 2 2 2 8 , = . Finally, the third excited state, corresponding to either
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