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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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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.
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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