Questions tagged [normalization]

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189 questions
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Solving time-independent Schrodinger equation with $V=0$

I recently came across this section in "Physical chemistry" by Peter Atkins and Julia Paula. There they discuss the solution of Schrodinger equation for a particle of mass m moving through a single ...
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Mathematics required for understanding quantum operators and the preservation of wave-function's norm [closed]

I am currently in High school and doing the IB curriculum. I just finished with my first year and moving on to my final year.As part of my highschool diploma, I have to complete an essay on any ...
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Interpretation of the propagator

In quantum mechanics, it is clear that $\langle x|y\rangle = 0$ for $x\ne y$, where $|x\rangle$ is the state with the particle at position $x$. (Notice that this $|x\rangle$ is different from the ...
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Normalizing Efficiencies with different motor power ratings

I have obtained data of the efficiencies of a few models of electric vehicles. We would like to compare them, but we have noted that the different motor power ratings may have an effect on the ...
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Dirac delta normalization of electromagnetic fields

Usually, to quantize electromagnetic fields we use box normalization and therefore the normalization constant contains the dimensions of Volume V of the box. But if we perform the Dirac-delta ...
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Why is there a factor of $\sqrt2$ listed for the neutral pion?

I was reading the Wikipedia page on pions. At the bottom of the page, there is a listing for the neutral pion ($\frac{\rm u\bar u+d\bar d}{\sqrt{2}}$). Why are they over the square root of 2? There ...
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'Show that $E$ must exceed $V(x)$ for every normalisable solution of the TISE'. Surely you can show that this isn't true using exponentials?

In Griffith's this is a question, there's the clear answer which jumps out immediately: $$\frac{d^2\psi}{dx^2} = \frac{2m}{\hbar^2}(V(x)-E)\psi.$$ That is, if E is less than V the second deriviative ...