1
vote
1answer
62 views

How to get the time derivative of an expectation value in quantum mechanics?

The textbook computes the time derivative of an expectation value as follows: $$\frac{d}{dt}\langle Q\rangle=\frac{d}{dt}\langle \Psi|\hat Q\Psi\rangle=\langle \frac{\partial\Psi}{\partial t}|\hat ...
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3answers
181 views

Ordering of differential operators

If we write something like: $\partial_a X_{\mu} \partial^a X^{\mu}$ Does that mean the first derivative is only applied to the first X? ($\partial_a X_{\mu})( \partial^a X^{\mu}$) Or is the ...
4
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2answers
1k views

Derivatives of operators

How do derivatives of operators work? Do they act on the terms in the derivative or do they just get "added to the tail"? Is there a conceptual way to understand this? For example: say you had the ...
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2answers
168 views

Notation for differential operators and wave function math

I know that $[\frac {d^2}{dx^2}]\psi$ is $\frac {d^2\psi}{dx^2}$ but what about this one $[\frac {d^2\psi}{dx^2}]\psi^*$? Is it this like $\frac {d^2\psi\psi^*}{dx^2}$ or this like $\frac ...
2
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2answers
960 views

Derivative of the product of operators

I'm asked to show that $\frac{d(\hat{A}\hat{B})}{d\lambda} = \frac{d\hat{A}}{d\lambda}\hat{B} + \hat{A}\frac{d\hat{b}}{d\lambda}$ With $\lambda$ a continuous parameter Should I use the definition ...