11.3 In dimensionless variables (h = 1, m = 1, and thus pj = ) the Hamilto- nian of a two-dimensional oscillator takes the form 1 1 H=D (p2 + p) + (1+6zy)(교? + y") 2 where we suppose that 8 « 1. Determine the wave functions for the three lowest lying energy levels in the case d = 0. Calculate the shift of these levels for 8 +0 in first-order perturbation theory. Note the degeneracy which occurs.
11.3 In dimensionless variables (h = 1, m = 1, and thus pj = ) the Hamilto- nian of a two-dimensional oscillator takes the form 1 1 H=D (p2 + p) + (1+6zy)(교? + y") 2 where we suppose that 8 « 1. Determine the wave functions for the three lowest lying energy levels in the case d = 0. Calculate the shift of these levels for 8 +0 in first-order perturbation theory. Note the degeneracy which occurs.
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Transcribed Image Text:11.3 In dimensionless variables (h = 1, m = 1, and thus pj = ) the Hamilto-
nian of a two-dimensional oscillator takes the form
II -, ( + r) + (1 + day)(x* + y*)
1
(1+ 8xy)(x² + y²)
Н —
where we suppose that 8 « 1. Determine the wave functions for the three lowest
lying energy levels in the case d = 0. Calculate the shift of these levels for 8 0 in
first-order perturbation theory. Note the degeneracy which occurs.
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