Quantum Chemistry

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Exercise. This is the solution to exercise 6.1 in the book.

Solution.

ψ(x,y,z) = AxAyAz sin nxπx a sin nyπy b sin nzπz c

We must have that

0a0b0cψ(x,y,z)ψ(x,y,z)dxdydz = 1

If we assign

AxAyAz = C

then

C20a sin2nxπx a dx0b sin2nyπy b dy0c sin2nzπz c dz = 1

or

C2a 2 b 2 c 2 = 1

Hence

C = 8 abc

Thus the normalization leads to

ψ(x,y,z) = 8 abcsin nxπx a sin nyπy b sin nzπz c