Eigenvectors eigenvalues and constant of motion

[umagongdi]

1. The problem statement, all variables and given/known data

a.) The motion of a particle in the 3-dimensional space is described by the Hamiltonian H = Hx+Hy+Hz, where

Hx=1/2*(px2+x2), Hy=1/2*(py2+y2), Hz=1/2*(pz2+z2)

Check that the standard angular momentum operators Lx, is a constant of motion.

b.) By knowing that the ground state wavefunction for Hx is proportional to e-x2/2, write the wavefunction Y0(x,y,z) representing the ground state for H (you are not required to fix the normaliszation of the wavefunctions in this problem).

2. Relevant equations



3. The attempt at a solution

a.) Do you need to check if L and H commute?
b.) I really don't have a clue any tips?

[G01]

1. The problem statement, all variables and given/known data

a.) The motion of a particle in the 3-dimensional space is described by the Hamiltonian H = Hx+Hy+Hz, where

Hx=1/2*(px2+x2), Hy=1/2*(py2+y2), Hz=1/2*(pz2+z2)

Check that the standard angular momentum operators Lx, is a constant of motion.

b.) By knowing that the ground state wavefunction for Hx is proportional to e-x2/2, write the wavefunction Y0(x,y,z) representing the ground state for H (you are not required to fix the normaliszation of the wavefunctions in this problem).

2. Relevant equations



3. The attempt at a solution

a.) Do you need to check if L and H commute?
b.) I really don't have a clue any tips?



a.) Do you need to check if L and H commute?

Can you relate that commutator to the equations of motions. HINT: Look up the Heisenberg equation of motion.

b.) I really don't have a clue any tips?

Assume the wave function can be separated in its variables.

[umagongdi]

Assume the wave function can be separated in its variables.

Oh i think i get it now thanks. You can just separate the wave function like this?

Y0(x,y,z)=e-x2/2+e-y2/2+e-z2/2