# Questions tagged [normalization]

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### Normalization of solution of Dirac equation

I know that the solution to the dirac equation are of the form: $\psi(x)=u(\vec{p})e^{ip\cdot x}$ and the spinor can be normalized as $u^\dagger u =E$. I was reading "Lectures on Quantum Field ...
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### How would I normalize this ket vector? [closed]

So I am given the vector: $$|Ψa⟩ = |x⟩ + |y⟩ − |z⟩$$ And I need to normalize it. I know that I have to take the dot product of the vector with itself (and it needs to equal 1) but how would I do this ...
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### A common standard model Lagrangian mistake?

A common standard model lagrangian is written in a cup like this. It appears in many places also on a T shirt. But isnt that there is an obvious mistake? That the Dirac lagrangian is already itself ...
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### Normalising a free particle wave function, at $t=0$

I am trying to normalise the wave function $\psi$ for a free particle, with initial boundary conditions. $$\Psi(x,0)=Ae^{-2|x|}.$$ When trying to normalise it, I keep getting $\infty$ which clearly ...
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### Questions about normalizing wavefunctions [closed]

learning QM and just have a few questions regarding normalizing wavefunctions. Thus far, every initial wavefunction that we've normalized has had an undefined constant explicitly put out front (i.e., ...
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### The Density Matrix of a Pure State

It is my understanding that any pure quantum state $|\psi\rangle$ can be represented by the density matrix $|\psi\rangle\langle\psi|$. It is also my understanding that $|\psi\rangle\langle\psi|$ ...
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### Probability of non-normalizable states

In the book Quantum Field Theory by Jakob Schwichtenberg, he is discussing about non-normalizable states in chapter 8. If you compute the normalization in $(8.67)$ you just get infinity. He said one ...
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### Proof of normalization constant of wave function to be independent of time

I am trying to prove that the normalization constant is independent of time. If we have fixed it for a particular time then it will remain constant for all time. Suppose $\psi(x,t)$ is a wavefunction. ...
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### How do I normalise the wavefunction of a hydrogen 1s orbital to obtain the normalisation constant?

The wavefunction I've been given for a 1s hydrogen orbital is: $$\Psi = A e^{-r}$$ And I need to normalize this to find the value of A. I understand to normalise this I would inset this wave ...
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### What is meant by a probablity given by $e^{-\text{P.E.}/kT}$ with $\text{P.E.}<0$?

This is from https://www.feynmanlectures.caltech.edu/I_40.html Let us take the case of just two molecules: the $e^{-\text{P.E.}/kT}$ would be the probability of finding them at various mutual ...
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### Understanding the Path Integral Formulation

Currently, I am reading chapter 3 of Condensed Matter Field Theory, which is on the Path Integral formulation of quantum mechanics. The book denotes $\Delta t = t/N$, where $t$ is the total time ...
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### Coefficients of the wave function - a free particle in a box [closed]

If we solve the time independent Schrödinger equation for a particle in a box of length $L$, we get: $$\psi_n\left(x\right)=A\sin\left(\frac{\pi n}{L}x\right)$$ I then see that we normalize $A$ such ...
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### $\int_{-\infty}^{\infty} |\psi(x)|^2 ~ dx = 1$ when $\psi(x) = C\exp\left(\frac{x^2}{2a^2} + \frac{ix^3}{3a^3}\right)$ [closed]

The information given is: Consider a state $|\psi\rangle$ describing a quantum particle on a line, whose position representation $\langle x|\psi\rangle = \psi(x)$ is given by: \begin{gather*} \...
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### Value of matrix elements between bound and unbound states

How do you assign a numerical value to the matrix element between states of the discrete part $|n\rangle$and the continuous parts $|\alpha\rangle$of a spectrum of an operator ? The states of the ...
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### Normalization of a wavefuntion [closed]

I am working with the following wavefuntion which describes two entangled photons. I need to normalize it over the frequency domain, $\omega_\alpha$ and $\omega_\beta$ are the frequency of the ...
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At the introduction to Yang-Mills-theory and its gauge group typically a $SU(N)$-group, the generators $t_A$ of the corresponding Lie-algebra are supposed to fulfill the following normalisation: Tr(...