Answer
See the detailed answer below.
Work Step by Step
When the box is oriented vertically in a strong gravitational field, as in our case on a neutron star, the gravitational pull will cause the particle to experience a strong force toward the bottom of the box.
This means the particle will move more slowly as it approaches the top of the box because of gravitational potential energy, and thus the wavelength will stretch toward the top, while the wave function will be compressed near the bottom of the box since the particle has more kinetic energy since it moves faster.
This means that the gravitational field causes a non-uniform motion (slowing the particles at the top and speeding them near the bottom) and hence the nodes will not be uniformly spaced.
Thus the standing wave will be like the one shown below.
