problems3

problems3 - (b The energy of the particle is measured at...

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Physics 4021: Introduction to Quantum Mechanics I Homework Assignment 3 Due in class: Thursday, Sept. 27, 2007 1. Problem 2.4 2. Problem 2.5 3. Problem 2.6 4. Problem 2.7 5. Problem 2.8 6. When time t < 0, a particle of mass m is in the ground state of the infinite square well with the potential = otherwise a x x V ) 0 ( 0 ) ( At t =0, suddenly the right side wall expands, so that the potential becomes = otherwise a x x V ) 2 0 ( 0 ) ( while the wave function (momentarily) undisturbed. (a) Find the expectation value of energy (Hint: there is a method in which you can obtain an exact expression rather than an infinite series).
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Unformatted text preview: (b) The energy of the particle is measured at t > 0. Find the value of most probable measured energy and its probability. (c) Show that the time dependent wavefunction return to its initial state ( t = 0) when . h π / 16 2 ma t = (d) Now, consider the same problem except the left wall moves rather than the right wall at t =0, such that ⎩ ⎨ ⎧ ∞ ≤ ≤ − = otherwise a x a x V ) ( ) ( Find the stationary wave functions and their energy values for this potential. Note that the potential energy is symmetric in this case. 1...
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This note was uploaded on 02/23/2010 for the course PHYS 4021 taught by Professor Kim during the Fall '08 term at Columbia.

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