The 2D infnite well: In two dimensions, the Schrodinger equation is

(a) Given that U is a constant, separate variables by trying a solution of the form ?(x, y) = f(x)g(y), then dividing by f(x)g(y). Call the separation constants C _x and C _Y .

(b) For an infinite well,

What should f(x) and g(y) be outside this well? What functions would be acceptable standing- wave solutions for f(x) and g(y) inside the well? Are C _x and C _y positive, negative, or zero?

Imposing appropriate conditions, find the allowed values of C _x and C _y .

(c) How many independent quantum numbers arc there?

(d) Find the allowed energies E.

(e)Are there energies for which there is not a unique corresponding wave function?

Transcribed Image Text:

(2²2 +2²2 ) 4(x, y) = dy² 2m(EU) ħ² -(x, y) U= 68 0 < x < L, 0 < y < L otherwise (2²2 +2²2 ) 4(x, y) = dy² 2m(EU) ħ² -(x, y) U= 68 0 < x < L, 0 < y < L otherwise

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a The 2 dimensional Schrodinger wave equation is Substitute the assumed form of solution Then Divide ... View the full answer