HW-4 - state (ground state), i.e. its wave function is...

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Physics 17 Due 10-23-09 Fall 2009 T. Tomboulis HOMEWORK # 4 Reading Assignment: SMM Ch. 6, Sections 6.1-6.5. Subsection ”Charge-Coupled Devices in 6.4 is optional. Problems: 1. SMM Ch. 6: #1 2. SMM Ch. 6: #2 3. SMM Ch. 6: #5 4. The Schr¨ odinger equation for a particle in a box (text-Section 6.4) shows that there is no level at zero energy, i.e. the particle cannot be at rest. Show that indeed a particle at rest in a box would violate the uncertainty principle. 5. An electron in a box makes a transition from the n = 2 state to the n = 1 state emitting light of λ = 690nm. What is the length of the box? 6. Consider a particle in a box of length L . (a) Suppose that at initial time t = 0 the particle is in the lowest possible energy
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Unformatted text preview: state (ground state), i.e. its wave function is given by ψ 1 ( x ) = r 2 L sin ± πx L ² (text p. 204-205, equations (6.18), (6.19) with n = 1). What is its wave function at a later time t ? (b) Suppose that at initial time t = 0 the particle is in the state described by the the wavefunction Ψ( x, 0) = A ψ 1 ( x ) + B ψ 3 ( x ) , where A , B are constants, i.e. a superposition of the ground state and the second excited level. (i) Is there any constraint on the constants A and B ? (ii) What is its wave function at a later time t ? (iii) Compute the probability of detecting the particle at a point x at time t . Is it t-dependent or t-independent? 1...
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This note was uploaded on 01/21/2010 for the course PHYS 17 taught by Professor Staff during the Fall '08 term at UCLA.

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