4. consider a particle constrained to move on the surface of a sphere of radius a. take the center of the sphere as the origin of coordinates. the potential is then of the form r a (a) give the hamiltonian operator for the particle in spherical coordinates, and write out the t-independent schroedinger equation. (b) to make life easy ignore the angular dependence of the potential, i. e., set u(0, o) uo, where uo is a constant. what are the energy levels?

as technology advances, new experiments often expose problems in accepted theories. c

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-lavira: )

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.