# Questions tagged [normalization]

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### Confusion Regarding the Propagator [duplicate]

To my understanding, the expression $$G^+=\theta(t_f-t_i)\langle x_f|\mathcal{\hat U}(t_f,t_i)|x_i\rangle$$ represents the probability amplitude that a particle starting at position $x_i$ at time $t_i$...
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### Normalization of the harmonic oscillator propagator

The propagator of a quantum system is defined by $$\mathcal{K}(t,x;\,t_{0},x_{0})\,\equiv\,\left\langle x\right|\hat{U}(t,\,t_{0})\left|x_{0}\right\rangle.$$ In this notation, the unitarity demands ...
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### When do we exclude non-normalizable solutions and when not?

I'm a bit confused on when we should keep any non-normalizable solutions and when not. What do I mean? Let's say that we have the free particle system. The energy eigenstates are not normalizable - ...
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### Normalized units versus dimensionless units

In a molecular dynamics code, suppose, the distances are expressed in units of a characteristic length of the simulated system, $R_0$. In some papers it is written as, " distances are normalized ...
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### Finding the parameter regime over which a phase transition is observable

Suppose, two variables $P$ and $Q$ follow a relation like, $P=AQ^n$, where $A$ is a constant. If this relation describes the phase diagram of a system obtained numerically, how can I determine the ...
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### What is the wavefunction of definite position? [duplicate]

Reading the quantum mechanics textbook we are told the wave function for a definite position at $a$ is $\psi(x)=\delta(x-a)$. Yet, also we are told that the probability must be $\int|\psi(x)|^2 dx$=1. ... 1 vote
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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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Say I have a state of two non-interacting fermions in some system, $$\Psi_{12}(x_1,x_2)=\frac{1}{\sqrt{2}}(\Psi_1(x_1)\Psi_2(x_2)+\Psi_1(x_2)\Psi_2(x_1))\otimes\frac{1}{\sqrt{2}}(\uparrow\downarrow-\... 1 vote 1 answer 94 views ### Probability for scattering event I am reading Schwartz QFT. On page 61 in eq (5.20) he gives an expression that describes the probability for a 2\to n scattering event to happen:$$dP=\frac{T}{V}\frac{1}{(2E_1)(2 E_2)}\left|\... 88 views

### 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 ...
1 vote
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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., ...
I have obtained a probability distribution for the observable $l$ which takes the form: $$\frac{dP}{dl}=\frac{(1-\sqrt{1-3l^{2}})^{2}}{l^{3}\sqrt{1-3l^{2}}}\exp\left[-\frac{4\pi}{9l^{2}}(1-3l^{2})^{3/... 1 vote 1 answer 101 views ### Kohn-Sham equations, Sakurai 3rd edition, possible typo? In Sakurai's quantum mechanics book 3rd edition page 448, equation 7.88, the book writes "Kohn and Sham found a way to derive a self-consistent approximation scheme, based on single particle ... 0 votes 1 answer 73 views ### Showing that a wavefunction in column form is normalised [closed] I am given the following wavefunction in column form: \psi = \begin{bmatrix} \frac{1}{4} \\ \sqrt{\frac{15}{16}}i \end{bmatrix}  And asked to show that it is normalised. As I understand it, the ... 3 votes 1 answer 295 views ### Why do we need to normalise states in quantum field theory? In QM its obvious that we need to normalise quantum states since their inner product squared represents a probability. This normalization leads to physical states in QM being represented by 'rays' of ... -1 votes 1 answer 49 views ### When do we normalize a wave equation? In what kind of problems/exercises? Why? I'studying quantum mechanics, and i haven't understand very well, when should we normalize the wave equation? And why must we normalize it? 1 vote 2 answers 406 views ### Factor 1/\sqrt{2\pi} in the normalization of wave function packet My book has started using the wave packet definition as follows (time independent form):$$\Psi(x) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} A(k) \ e^{ikx}dx$$I do not understand where the 1/\... 2 votes 0 answers 89 views ### Normalization in vector field in QFT after non-relativistic expansion I encountered this equation when I was reading the article "Black Hole Superradiance Signatures of Ultralight Vectors"$$A_\mu=\frac{1}{\sqrt{2m}}\Big(\psi_\mu (\vec{r})\exp(-i\omega t)+\...
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 $|\psi\rangle\langle\psi|$ ...