For a spinless non-relativistic particle of mass m in a one-dimensional potential V (x) the Hamiltonia is H = + V (2) a) Express the Hamiltonian H in the basis formed by the position eigenvectors. b) show that [x,p]=iħ1 for the first two dimensions, and extract from this the relationship between the variables a and b /1 0 0 /01 0 H=a0 3 0 and X = b 1 0 √2 0 0 5/ 0 √20 c) In the basis formed by the energy eigenvectors, the system is in a state of 1 3t evaluate and explain the potential energy V(x) of the system.
For a spinless non-relativistic particle of mass m in a one-dimensional potential V (x) the Hamiltonia is H = + V (2) a) Express the Hamiltonian H in the basis formed by the position eigenvectors. b) show that [x,p]=iħ1 for the first two dimensions, and extract from this the relationship between the variables a and b /1 0 0 /01 0 H=a0 3 0 and X = b 1 0 √2 0 0 5/ 0 √20 c) In the basis formed by the energy eigenvectors, the system is in a state of 1 3t evaluate and explain the potential energy V(x) of the system.
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Transcribed Image Text:For a spinless non-relativistic particle of mass m in a one-dimensional potential V (x) the Hamiltonian
is
H
2M
a) Express the Hamiltonian H in the basis formed by the position eigenvectors.
b) show that [x,pl=ih1 for the first two dimensions, and extract from this the relationship
between the variables a and b
/0
1 0 0y
H= a0 3 0 and X = b 1
0 0 5/
1
0 v2
c) In the basis formed by the energy eigenvectors, the system is in a state of
1
3i
V3
evaluate and explain the potential energy V(x) of the system.
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