Tell me more ×  I am reading Shankar's Quantum Mechanics and I
am looking at the case where there is one particle inside a box,
where the potential is zero inside the wall and abruptly goes to
infinity outside the wall. I like the technique of differential
equations used and I am wondering if we suppose there is a
particle in $n$-dimensional space, then we can still use the
technique used in calculating wavefunction and energy in say a
2-dimensional and 3-dimensional box.  share|improve this
question add comment  1 Answer  up vote 3 down vote accepted
Yes, for infinite potential wells in any number of dimensions,
the same technique can be applied. Each confinement direction
gives an extra quantum number, and the wavefunction is just the
product of the 1D wavefunction for each direction.  More
problematic is the finite potential well, because one can't use
a simple expression for the potential in more than 1 dimension,
making the equations very hard to solve.  share|improve this
answer Just to add some precis