Use your generic solution to the 2D box wavefunctions to demonstrate the following prop- erties of wavefunctions. 1. Show that if you independently normalize (x) and (y) that the product of V(x) and (y) is also normalized. 2. Show that the wavefunctions for one dimension are orthogonal. Orthogonality means that ₁ndr = 6mn, where the Kroenecker delta function means that the function is one for men and zero for m‡n. m
Use your generic solution to the 2D box wavefunctions to demonstrate the following prop- erties of wavefunctions. 1. Show that if you independently normalize (x) and (y) that the product of V(x) and (y) is also normalized. 2. Show that the wavefunctions for one dimension are orthogonal. Orthogonality means that ₁ndr = 6mn, where the Kroenecker delta function means that the function is one for men and zero for m‡n. m
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Transcribed Image Text:Use your generic solution to the 2D box wavefunctions to demonstrate the following prop-
erties of wavefunctions.
1. Show that if you independently normalize (x) and (y) that the product of (x)
and (y) is also normalized.
2. Show that the wavefunctions for one dimension are orthogonal. Orthogonality means
that f₁ Vndr = Smn, where the Kroenecker delta function means that the function
is one for men and zero for m‡n.
m
3. How many quantum numbers are needed to describe the energy of your system?
4. Show that the two dimensional wavefunctions are orthogonal by performing this test
on the wavefunction for n = 1, ny = 2 and the wavefunction for nr = 2 and ny = 1.
CLx Ly
Mathematically the operations looks like f¹* f¹¹ V₁,2 (x, y) V2,1 (x, y) dxdy.
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