1
vote
1answer
64 views

differential equation of the square root of a matrix

If the differential equation governing the time dependent matrix $M(t)$ is $\frac{dM(t)}{dt}=A.M(t).B$ or $\frac{dM(t)}{dt}=A.M(t)+M(t).A$ where $A$ and $B$ are constant matrices, what is the ...
1
vote
0answers
34 views

Find the probability that a measurement results in a certain interval

I was given this problem: Let the state $f(x)=e^{-|x|}$ and an operator $P=-i\frac{d}{dx}$. (a) What is the probability that a measure of P results in the interval $[0,1]$ (b) What is the Fourier ...
5
votes
2answers
402 views

Regarding Ladder Operators and Quantum Harmonic Oscillators

When dealing with the Quantum Harmonic Oscillator Operator $H=-\frac{d^{2}}{dx^{2}}+x^{2}$, there is the approach of using the Ladder Operator: Suppose that are two operators $L^{+}$ and $L^{-}$ and ...