Consider a free particle constrained to move over the rectangular region 0 x a, 0 y
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Question:
Consider a free particle constrained to move over the rectangular region 0≤ x ≤a, 0≤ y ≤ b.
The energy eigenfunctions, i.e. wavefunctions, of this system are:
The Hamiltonian for the system is:
a. Show that if the system is in one of its eigenstates, then 〈E2 〉-〈E〉2 = 0
b. The energy equation for this system is
Construct an energy level diagram (include the first five energy levels) if the particle is constrained to a square (a=b). Don't forget degeneracy.
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