Consider a two-dimensional infinite rectangular well, with a potential given by 0 V (x, y) = { } 0≤x≤a; 0 ≤ y ≤b otherwise Using separation of variables in cartesian coordinates (as worked out in class for the 3-dimensional case) (a) Find the stationary states and corresponding energy eigenvalues (b) Write down the first 5 distinct energy eigenstates for the case b = a. (c) How would your answer to (b) above change if b = 2a?
Consider a two-dimensional infinite rectangular well, with a potential given by 0 V (x, y) = { } 0≤x≤a; 0 ≤ y ≤b otherwise Using separation of variables in cartesian coordinates (as worked out in class for the 3-dimensional case) (a) Find the stationary states and corresponding energy eigenvalues (b) Write down the first 5 distinct energy eigenstates for the case b = a. (c) How would your answer to (b) above change if b = 2a?
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Transcribed Image Text:Consider a two-dimensional infinite rectangular well, with a potential given by
V (x, y) = {
0 0 ≤ x ≤ a; 0 ≤ y ≤b
otherwise
Using separation of variables in cartesian coordinates (as worked out in class for the 3-dimensional case)
:{%
Find the stationary states and corresponding energy eigenvalues
(b) Write down the first 5 distinct energy eigenstates for the case b = a.
How would your answer to (b) above change if b = 2a?
(d) Write down the first 5 distinct energy eigenstates for the case b » a.
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