Find zero angular momentum, normalized energy eigenstates, and the energy eigenvalues, by solving the radial equation.

(See attached file for full problem description)

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2. A particle of mass m is constrained to move between two concentric, impermeable spheres of radii r = a and r = b. The potential V( r ) = 0 between the spheres (a<r<b), and V(r) = otherwise. Find all of the zero angular momentum (l = 0) normalized energy eigenstates, and the energy eigenvalues, by solving the radial equation

See the attached files.
1. Operator Algebra. Evaluate the following expressions:
See attached for equations
Neutrino Oscillation made oversample. Neutrinos come in three varieties that we know of: the electron neutrino (V_e) the tau neutrino (V_T) andthe muon neutrino (which is irrelevant to this problem). Nuclear fusi

1. show that the commutator obeys:
[A,B] = -[B,A]
[A,B+C]=[A,B] + [A,C]
[A,BC]=[A,B]C+B[A,C]
[A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0
Given the fundamental commutator relation between momentum and position [x,p] = ih
show that:
a. [x^n,p] = ihn*x^(n-1)
b. [x,p^n] = ihn*p^(n-1)
c. show that if f(x) can be expanded in polyno

A meteor is moving at a speed of 32000 km/hr relative to the centre of Earth at a point
560 km from the surface of the Earth. At this time it has a radial velocity of 6400 km/hr.
How close does it come to the Earth's surface? (RE =6373 km)

Mass m whirls on a frictionless table, held to circular motion by a string which passes through a hole in the table. The string is slowly pulled through the hole so that the radius of the circle changes from L1 to L2.
Show that the work done in pulling the string equals the increase in kinetic energy of the mass.

Consider the corresponding problem for a particle confined to the right-hand half of a harmonic-oscillator potential:
V(x) = infinity, x< 0
V(x) = (1/2)Cx^2, x >= 0
a. Compute the allowed wave function for stationary states of this system with those for a normal harmonic oscillator having the

Hydrogen atom
Theradial probability density for an electron is r2R2(r). That means that the probability of finding an electron at a certain radius r within a radial thickness dr is dr* r2R2(r) for an infinitely thin shell and approximately r* r2avg R2(ravg) for a shell of finite thickness r.
The quantity ravg is some average

Please assist me in solvingthe following problems:
Let's consider an ion (in an effective spin state corresponding to s = 1) at a crystal lattice site. As for the effective potential seen by the ion, assume spin Hamiltonian of the form:
H = alpha*S^2_z + beta*(S^2_z - S^2_y)
where alpha and beta are some real con

See attached graphic.
A small asteroid is moving in a circular orbit of radius R_0 about the sun. This asteroid is suddenly struck by another asteroid. (We won't worry about what happens to the second asteroid, and we'll assume that the first asteroid does not acquire a high enough velocity to escape from the sun's gravity).

A student on a piano stool rotates freely with an angular speed of 3.16 rev/s. The student holds a 1.50 kg mass in each outstretched arm, 0.794 m from the axis of rotation. The combined moment of inertia of the student andthe stool, ignoring the two masses, is 5.45 kg*m2, a value that remains constant. As the student pulls his