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adiputra
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1) The problem is about finding the ground state energy of electron in an infinite 2D circular and square potential well with the same area. I have calculate it via method of separation of variables in polar and cartesian coordinate respectively, and it is found out that the one on the circular well has lower energy(confirm to be correct). But, then the question ask why, as in why is it lower? any physical significance causing that? I heard this is the Uni. Berkeley graduate interview question?
2) Since I am on this question, I remember last time one of my lecturer talking about 1D infinite squae well with length L and I forget what is the physical significance to why as L decrease the ground state energy increase (E=h^2/8mL^2)? If i am not wrong, my lecturer say something like as L decrease, the energy is squeezed into a smaller dimension kind of stuff... but then i don't think it is correct as that reasoning talk about energy density.
2) Since I am on this question, I remember last time one of my lecturer talking about 1D infinite squae well with length L and I forget what is the physical significance to why as L decrease the ground state energy increase (E=h^2/8mL^2)? If i am not wrong, my lecturer say something like as L decrease, the energy is squeezed into a smaller dimension kind of stuff... but then i don't think it is correct as that reasoning talk about energy density.