348-problem31 - need two quantum numbers to specify each...

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Chem. 540 Instructor: Nancy Makri PROBLEM 31 Consider a quantum mechanical particle moving in two dimensions with the following Hamiltonian: 2 2 ˆ ˆ ˆ ˆ ˆ ( , ) 2 2 y x p p H V x y m m = + + , where 2 2 2 2 1 1 ˆ ˆ ˆ ˆ ( , ) 2 2 x y V x y m x m y ϖ = + . a) Sketch this potential and write out the energy eigenvalues for this system. Notice that you
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Unformatted text preview: need two quantum numbers to specify each state. Are there degenerate levels? b) Now suppose that 2 x y = . Make a diagram of the six lowest energy states of the system, labeling the states and indicating the corresponding energy levels....
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