A particle moves in 5 dimensional space (x, y, z, u, v). Its Hamiltonian is given by
where the space is infinite in all directions except v which is
confined between v = 0 and v = a. Assume that the wave function
vanishes at v = 0 and v = a. Further, 
= |E| 1 /~ 2 , where |E1| is the absolute value of the Hydrogen
ground state energy.
(d) What are the eigenstates of this Hamiltonian in the y, z, u directions? What is the energy of the ground state of this system?
Please answer the above first. The following is the least important to answer:
(c) What are the eigenstates of this Hamiltonian in the x and v directions?
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A particle moves in 5 dimensional space (x, y, z, u, v). Its
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