III-6: The inertia of a planar rotor isI, its angular momentum L is quantized as L=- with o as rotation angle, the Hamiltonian for the quantized rotor is H==-1 %3D 72 02 %3D (a) prove the commutation relations [6, L] = ih , [L, H] =0; (b) find the stationary eigen-state energies and wave functions; (c) whether the stationary energy levels are degenerate or not? %3D
III-6: The inertia of a planar rotor isI, its angular momentum L is quantized as L=- with o as rotation angle, the Hamiltonian for the quantized rotor is H==-1 %3D 72 02 %3D (a) prove the commutation relations [6, L] = ih , [L, H] =0; (b) find the stationary eigen-state energies and wave functions; (c) whether the stationary energy levels are degenerate or not? %3D
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![III-6: The inertia of a planar rotor is I, its angular momentum
L is quantized as L=-ih
with o as rotation angle, the Hamiltonian for the quantized rotor
is H= =-
712 02
21 a02
%3D
(a) prove the commutation relations [ø, L] = ih , [L, H] = 0 ;
(b) find the stationary eigen-state energies and wave functions;
(c) whether the stationary energy levels are degenerate or not?
(d) whether stationary wave functions are eigen-states of the
angular-momentum operator?
III-1: Use the expression of the probability current, to prove E-
q. (239) of the square barrier potential.
Jieft = v (1 - |R|2),
(239)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb70807a4-ae83-4014-ada1-2ec456c17447%2F525852cb-b2fc-4b90-a81b-d137f1f9cf75%2Fe23xar_processed.jpeg&w=3840&q=75)
Transcribed Image Text:III-6: The inertia of a planar rotor is I, its angular momentum
L is quantized as L=-ih
with o as rotation angle, the Hamiltonian for the quantized rotor
is H= =-
712 02
21 a02
%3D
(a) prove the commutation relations [ø, L] = ih , [L, H] = 0 ;
(b) find the stationary eigen-state energies and wave functions;
(c) whether the stationary energy levels are degenerate or not?
(d) whether stationary wave functions are eigen-states of the
angular-momentum operator?
III-1: Use the expression of the probability current, to prove E-
q. (239) of the square barrier potential.
Jieft = v (1 - |R|2),
(239)
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