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ultimateguy
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[SOLVED] Virial Theorem
A particle has a potential [tex]\lambda X^n[/tex] and Hamiltonian [tex]H = \frac{P^2}{2m} + V(x)[/tex]
Knowing that the commutator of H and XP is [tex]i\hbar(n\lambda X^n - \frac{P^2}{m})[/tex], find the average values <T> and <V> and verify that they satisfy:
[tex]2<T>=n<V>[/tex]
The question asked to calculate the commutator and that is what I found, but I'm lost as to how to get the average values and proove the inequality.
Homework Statement
A particle has a potential [tex]\lambda X^n[/tex] and Hamiltonian [tex]H = \frac{P^2}{2m} + V(x)[/tex]
Knowing that the commutator of H and XP is [tex]i\hbar(n\lambda X^n - \frac{P^2}{m})[/tex], find the average values <T> and <V> and verify that they satisfy:
[tex]2<T>=n<V>[/tex]
Homework Equations
The Attempt at a Solution
The question asked to calculate the commutator and that is what I found, but I'm lost as to how to get the average values and proove the inequality.
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