Physics 741 Graduate Quantum Mechanics 1
Solution Set Q
1. [10] In chapter nine, section A, we were searching for matrices D ( R ) which satisfy
D ( R1 ) D ( R2 ) = D ( R1R2 )
One easy way to make thi
Physics 742 Graduate Quantum Mechanics 2
Solution Set Q
1. [15] A spin particle of mass m lies in a one-dimensional spin-dependant potential H0 = P2 1 + m 2Q 2 P+ 2m 2 where 1 0 P+ = . 0 0
In other wo
Physics 741 Graduate Quantum Mechanics 1
Solution Set P
1. [30] In class we solved the hydrogen atom, which is a spherical 1/r potential. Consider another spherically symmetric potential, namely, the
Physics 742 Graduate Quantum Mechanics 2
Solution Set P
1. [25] A hydrogen atom is in interstellar space in the 1s state, but not in the true ground state (F = 0), but rather in the hyperfine excited
Physics 741 Graduate Quantum Mechanics 1
Homework Set O Due Wednesday, October 15
1. [10] Two particles interacting via a spherically symmetric relative potential have Hamiltonian
P12 P22 H= + + V ( Q
Physics 742 Graduate Quantum Mechanics 2
Solution Set O
1. [20] A hydrogen atom is in the 1s ground state while being bathed in light of sufficient frequency to excite it to the n = 2 states. The ligh
Physics 741 Graduate Quantum Mechanics 1
Solution Set N
1. [10] Let J = J x , J y , J z be three Hermitian operators that commute with the Hamiltonian H, and have angular momentum-like commutation rel
Physics 742 Graduate Quantum Mechanics 2
Solution Set N
1. [15] A particle of mass m is initially in the ground state of a harmonic oscillator with frequency . At time t = 0, a perturbation is suddenl
Physics 741 Graduate Quantum Mechanics 1
Solution Set M
1. [20] A particle of mass m and energy E in two dimensions is incident on a plane step function given by
0 if Qx < 0, V ( Qx , Qy ) = V0 if Qx
Physics 742 Graduate Quantum Mechanics 2
Homework Set M
1. [5] Tritium is 3H an isotope of hydrogen which radioactively decays to 3He. Assume an isolated 3H has its electron in the ground state when i
Physics 741 Graduate Quantum Mechanics 1
Solution Set L
1. [10] In class we found the even parity bound states for H= P2 + V (Q ) , 2m where
0 V (Q ) = V0
if Q < a if Q > a
Repeat the analysis for t
Physics 742 Graduate Quantum Mechanics 2
Solution Set L
1. [25] A particle of mass m scatters from a potential
V ( r ) = F ( r a )
so that the potential exists only at the surface of a narrow sphere o
Physics 741 Graduate Quantum Mechanics 1
Solution Set K
1. [10] At t = 0, a single particle is placed in a harmonic oscillator
H = P 2 2m + 1 m 2Q 2 2
in the superposition state
3 4 (t = 0) = 5 1 + 5
Physics 742 Graduate Quantum Mechanics 2
Solution Set K
1. [15] An electron of mass m scatters from a neutral hydrogen atom in the ground state located at the origin. (a) [7] What is the charge distri
Physics 741 Graduate Quantum Mechanics 1
Solution Set J Due Friday, September 26
1. [15] A particle of mass m lies in a one-dimensional infinite square well in the region [0,a]. At t = 0, the wave fun