237module9 - equation for a particle of mass m in this...

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Quantum Mechanics I - Module 9 Review Questions Try to answer the following questions as preparation for the coming exam. 1. What physical requirement (i.e. constraint on the wavefunction) leads to quantization of the energy levels in the 1-D simple harmonic oscillator? 2. The simple harmonic oscillator has a nonzero ground state energy. Why can’t the ground state have zero energy? 3. Consider the three dimensional harmonic oscillator with a potential given by: V ( x, y, z ) = 1 2 2 x x 2 + 1 2 2 y y 2 + 1 2 2 z z 2 . (a) Write down the three dimensional time independent Schroedinger
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Unformatted text preview: equation for a particle of mass m in this potential. (b) How many quantum numbers are required to specify a stationary state of this system? (c) Write down an expression for the energy eigenvalues of this system. (d) Assume that ω x = ω y = 2 ω z . Make a table of the first eight distinct eigenenergies of the system, indicate the relevant quantum numbers, and indicate clearly which values are degenerate. 1...
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