508 Quantum MechanicsP41.45(a)fEh==×⋅×FHGIKJ=×−−1806626 10160 10434 10341914....eVJsJ1.00 eVHzafej(b)λ××=−cf300 10691 106918147...msHzm nm(c)∆∆Et≥=2so ∆Etht≥==×=×−−−−=2442 00 102 64 101 65 103462910πaf....sJ eV*P41.46(a)Taking LLLxy, we see that the expression for EbecomesEhmLnne=+22228.For a normalizable wave function describing a particle, neither nxnor nycan be zero. Theground state, corresponding to 1, has an energy ofEhhee11222284,=.The first excited state, corresponding to either nx=2, ny=1 or nx=1, ny=2 , has an energyEEhh21122222858,,+=.The second excited state, corresponding to nx=ny=2 has an energy ofEhh22228,=.Finally, the third excited state, corresponding to either
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