Question

1) Two particle Hamiltonian Consider the Hamiltonian for a system of two identical particles that may be interacting with one another \hat{H} = \frac{\hat{p}_1^2}{2m} + \frac{\hat{p}_2^2}{2m} + V(x_1, x_2) a. Argue or show that if the two particles are identical, $V(x_1, x_2) = V(x_2, x_1)$ b. Evaluate the commutation relation $[\hat{H}, \hat{p}_{12}]$. What does your answer tell you? c. A quantum system of two identical particles starts out in a symmetric state and evolves in time. How does the symmetry change as a function of time?

          1) Two particle Hamiltonian
Consider the Hamiltonian for a system of two identical particles that may be interacting with
one another
\hat{H} = \frac{\hat{p}_1^2}{2m} + \frac{\hat{p}_2^2}{2m} + V(x_1, x_2)
a. Argue or show that if the two particles are identical, $V(x_1, x_2) = V(x_2, x_1)$
b. Evaluate the commutation relation $[\hat{H}, \hat{p}_{12}]$. What does your answer tell you?
c. A quantum system of two identical particles starts out in a symmetric state and
evolves in time. How does the symmetry change as a function of time?

1) Two particle Hamiltonian
Consider the Hamiltonian for a system of two identical particles that may be interacting with
one another
Ĥ = (p̂1^2)/(2m) + (p̂2^2)/(2m) + V(x1, x2)
a. Argue or show that if the two particles are identical, V(x1, x2) = V(x2, x1)
b. Evaluate the commutation relation [Ĥ, p̂12]. What does your answer tell you?
c. A quantum system of two identical particles starts out in a symmetric state and
evolves in time. How does the symmetry change as a function of time?

Added by Mark E.

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