- #1
Monci
- 8
- 4
Homework Statement
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I'm trying to solve the following problem. (a) was easy but I am stuck at (b).
Homework Equations
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Since we are told that the Hamiltonian is conserved, and the answer is in terms of the uncertainty of H, I assume I have to use the conservation of uncertainty. Maybe I could use the Schrödinger equation to see how time affects the wave function.
The Attempt at a Solution
Using the Schrödinger equation I have $$\psi (t) = \psi (0) + \frac{1}{i\hbar}H\psi(0)t + O(t^2)$$
However I don't find this particularly useful since I can't get from here to the uncertainty of H easily. I have tried the case with just two states but didn't accomplish anything. Dimensional analysis suggests something like $$ 1 - \frac{\Delta H^2}{\hbar^2}dt^2 + O(t^3) $$
I have no idea how to proceed.