Quantum Confined Particle Motion: Shape of Wave Function on a Sphere

1. For linear motion, you have seen how the deBroglie wavelength changes as the momentum of the particle changes (e.g. number of nodes for PIB). Consider a particle confined to the surface of a sphere, which can be described by the rigid rotator model. What do you expect for the shape of the wave function describing a pole-to-pole motion? (A) nodes form “circles of latitude” on the sphere; the number of nodes increases with angular momentum (B) nodes form “circles of latitude” on the sphere; the number of nodes decreases with angular momentum (C) nodes form “circles of longitude” on the sphere; the number of nodes increases with angular momentum (D) nodes form “circles of longitude” on the sphere; the number of nodes decreases with angular momentum

2. For linear motion, you have seen how the deBroglie wavelength changes as the momentum of the particle changes (e.g. number of nodes for PIB). Consider a particle confined to the surface of a sphere, which can be described by the rigid rotator model. What do you expect for the shape of the wave function describing a pole-to-pole motion? (A) nodes form “circles of latitude” on the sphere; the number of nodes increases with angular momentum ... nodal lines are always perpendicular to the direction of motion (B) nodes form “circles of latitude” on the sphere; the number of nodes decreases with angular momentum (C) nodes form “circles of longitude” on the sphere; the number of nodes increases with angular momentum (D) nodes form “circles of longitude” on the sphere; the number of nodes decreases with angular momentum