1155_Physics ProblemsTechnical Physics

1155_Physics ProblemsTechnical Physics - 496 *P41.12...

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496 Quantum Mechanics *P41.12 (a) The energies of the confined electron are E h mL n n e = 2 2 2 8 . Its energy gain in the quantum jump from state 1 to state 4 is h e 2 2 22 8 41 ej and this is the photon energy: h hf hc e 2 2 15 8 == λ . Then 8 15 2 mcL h e = and L h mc e = F H G I K J 15 8 12 . (b) Let represent the wavelength of the photon emitted: hc h h h ee e =−= 2 2 2 2 2 2 2 2 8 4 8 2 12 8 . Then hc hc hm L h e e 15 8 81 2 5 4 and ′= λλ 125 .. Section 41.3 The Particle Under Boundary Conditions Section 41.4 The Schrödinger Equation P41.13 We have ψ ω = Ae ikx t bg and =− 2 2 2 x k . Schrödinger’s equation: 2 2 2 2 2 ψψ x k m EU = a f . Since k p h p 2 2 2 2 2 2 2 2 2 = π a f = and p m −= 2 2 . Thus this equation balances. P41.14 xA k xBk x af =+ cos sin + x kA kx kB kx sin cos 2 2 x k A kx k B kx cos sin −− = + 2 m mE Ak x Bk x = = a f cos sin Therefore the Schrödinger equation is satisfied if F H G I K J 2 2 x m = or −+ = F H G I K J + kA k xB k x mE x
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