Answer to Problem 3.37P The proof for virial theorem is given. Explanation of Solution Using Equation 3.73, LHS of the given expression can be written as, ar (xp) = ([H, xpl) + < d(xp)/dt> ? = ([H, x]p+x[H, p]} Here, x is the position operator, p is the momentum operator and H is the Hamiltonian operator. Write the expression for Hamiltonian. H = m + V (x) Using the expression for H and the commutator relation between x and p,
Answer to Problem 3.37P The proof for virial theorem is given. Explanation of Solution Using Equation 3.73, LHS of the given expression can be written as, ar (xp) = ([H, xpl) + < d(xp)/dt> ? = ([H, x]p+x[H, p]} Here, x is the position operator, p is the momentum operator and H is the Hamiltonian operator. Write the expression for Hamiltonian. H = m + V (x) Using the expression for H and the commutator relation between x and p,
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In the solution here to problem 3.37 Griffiths, the first step is to use Eqn 3.73*
Can you show me why <d(xp)/dt> = 0 or why it isn't in the RHS of the equation? (see my image)
* Equation 3.73: d<Q>/dt = (i/h_bar) <[H,Q]> + <dQ/dt>
![Answer to Problem 3.37P
The proof for virial theorem is given.
Explanation of Solution
Using Equation 3.73, LHS of the given expression can be written as,
ar (xp) = (IH, xp]) + < d(xp)/dt> ?
= {[H, x]p+x[H,p]}
Here, x is the position operator, p is the momentum operator and H is the Hamiltonian operator.
Write the expression for Hamiltonian.
H =
2m
+ V (x)
Using the expression for H and the commutator relation between x and p,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F169b6fc8-2ae4-41a1-9ae3-9a43efc049ab%2Fc0f79f46-8f7e-4db2-85a7-d63528078176%2Fson8at1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Answer to Problem 3.37P
The proof for virial theorem is given.
Explanation of Solution
Using Equation 3.73, LHS of the given expression can be written as,
ar (xp) = (IH, xp]) + < d(xp)/dt> ?
= {[H, x]p+x[H,p]}
Here, x is the position operator, p is the momentum operator and H is the Hamiltonian operator.
Write the expression for Hamiltonian.
H =
2m
+ V (x)
Using the expression for H and the commutator relation between x and p,
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