Questions tagged [normalization]
The normalization tag has no usage guidance.
295
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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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How to normalize a two-particle state?
Say I have a state of two non-interacting fermions in some system,
$$\Psi_{12}(x_1,x_2)=\frac{1}{\sqrt{2}}(\Psi_1(x_1)\Psi_2(x_2)+\Psi_1(x_2)\Psi_2(x_1))\otimes\frac{1}{\sqrt{2}}(\uparrow\downarrow-\...
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Probability for scattering event
I am reading Schwartz QFT. On page 61 in eq (5.20) he gives an expression that describes the probability for a $2\to n$ scattering event to happen:
$$dP=\frac{T}{V}\frac{1}{(2E_1)(2 E_2)}\left|\...
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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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Normalizable, but singular distribution
I have obtained a probability distribution for the observable $l$ which takes the form:
$$ \frac{dP}{dl}=\frac{(1-\sqrt{1-3l^{2}})^{2}}{l^{3}\sqrt{1-3l^{2}}}\exp\left[-\frac{4\pi}{9l^{2}}(1-3l^{2})^{3/...
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Kohn-Sham equations, Sakurai 3rd edition, possible typo?
In Sakurai's quantum mechanics book 3rd edition page 448, equation 7.88, the book writes
"Kohn and Sham found a way to derive a self-consistent approximation scheme, based on single particle ...
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Showing that a wavefunction in column form is normalised [closed]
I am given the following wavefunction in column form:
$\psi = \begin{bmatrix} \frac{1}{4} \\ \sqrt{\frac{15}{16}}i \end{bmatrix} $
And asked to show that it is normalised.
As I understand it, the ...
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Why do we need to normalise states in quantum field theory?
In QM its obvious that we need to normalise quantum states since their inner product squared represents a probability. This normalization leads to physical states in QM being represented by 'rays' of ...
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When do we normalize a wave equation? In what kind of problems/exercises? Why?
I'studying quantum mechanics, and i haven't understand very well, when should we normalize the wave equation?
And why must we normalize it?
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Factor $1/\sqrt{2\pi}$ in the normalization of wave function packet
My book has started using the wave packet definition as follows (time independent form):
$$\Psi(x) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} A(k) \ e^{ikx}dx$$
I do not understand where the $1/\...
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Normalization in vector field in QFT after non-relativistic expansion
I encountered this equation when I was reading the article "Black Hole Superradiance Signatures of Ultralight Vectors"
$$A_\mu=\frac{1}{\sqrt{2m}}\Big(\psi_\mu (\vec{r})\exp(-i\omega t)+\...
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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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Proving that the normalization is independent of time
The function that I want to normalize represents an Airy wave-packet:
$$\psi(x,t)=\mathrm{Ai}[q(x-ut+ivt-\tfrac12at^2)]e^{i\frac{mat}{\hbar}(x-ut-\frac13at^2)}e^{\frac{mv}{\hbar}(x-ut+\frac i2vt-at^2)}...
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Normalization problem of periodic wave function
So, I want to normalize the eigen wavefunctions of the momentum operator ($-i\hbar \frac{\partial}{\partial x}\psi(x)=p\cdot\psi(x)$ where $p$ is a real number).
The solution is $\psi(x)_p=C\cdot e^{\...
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What is $\langle 0|p\rangle$?
$\hat{p}$ is the generator of the translation group, so $$|r\rangle=e^{-ir\hat{p}/\hbar}|0\rangle\to\langle p|r\rangle=e^{-irp/\hbar}\langle p|0\rangle.$$ Assuming normalized position states
\begin{...
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Factor $\frac{1}{2}$ in scalar kinetic Lagrangian in QFT [duplicate]
Why is it that sometimes I see kinetic term of scalar Lagrangians written like this $$\mathcal{L}=\partial_\mu\phi^\dagger\partial^\mu\phi+\dots$$ like for example in scalar electrodynamics, while ...
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Normalization of One-Particle States for Klein-Gordon Field Quantization
Peskin & Schroeder in their QFT textbook discusses how we may normalize one-particle states $|\textbf{p}\rangle$ for Klein-Gordon field quantization in pages 22-23. The excerpts are given below.
...
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Normalisation in Dirac Notation
Say I have a wave function as follows (example):
$$|\psi\rangle=|\phi_1\rangle-\sqrt{3}|\phi_2\rangle+ 2i|\phi_3\rangle$$
I know normalisation means:
$$\langle \Psi_N|\Psi_N \rangle =1\tag{1}$$
I know ...
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'Normalization' of free particle wave function [duplicate]
I'm trying to obtain the expression for the free particle that is known $$\psi_p(x)=\frac{1}{\sqrt{2\pi\hbar}}e^{i\frac{xp}{\hbar}}$$
Easily you can arrive to the exponential,
$$p\langle x|p\rangle=-i\...
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How to normalize a linear combination of spherical harmonics?
I know the formula for normalizing individual spherical harmonics, but do not know how to normalize linear combinations of them
Say I have a system
$ \alpha (\theta, \phi) = aY_{l_1}^{m_1} + bY_{l_2}^...
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Can $n$ be negative for the infinite square well wave function $\psi_n(x)$?
Consider the classic particle in a box example (infinite square well) in quantum mechanics:
\begin{equation}
\psi_n(x)=A\sin(k_n x),
\end{equation}
where
\begin{equation}
k_n=\frac{n \pi}{L}.
\end{...
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Restricting the range of $x$ to normalize the wavefunction
I have a system in nuclear physics which can be approximated by two coupled harmonic oscillators (the Hamiltonian is a bit peculiar though.) I will denote their spatial coordinates by $x$ and $y$.
I ...
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LSZ formula in Srednicki, normalization issue
In the Ch.5 of his book, Srednicki says LSZ formula is valid provided the following conditions hold:
$$
\langle 0|\phi(x)|0\rangle = 0, \langle p|\phi(x)|0\rangle = 1
$$
To achieve these conditions, ...
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Using separation of variables to solve Schrödinger equation for a free particle
I was reading Introduction to Quantum Mechanics by David Griffiths and I am in Chapter 2, page 45. I know that since the solutions from Schrödinger equation cannot be normalized for a free particle. ...
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Weinberg's normalization convention for momentum eigenstates
In this answer https://physics.stackexchange.com/a/376193/274751 two different conventions for the normalization of momentum eigenstates are mentioned.
This convention amounts to the choice of $N(p)$ ...
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The normalization of the momentum eigenfunction [duplicate]
If the momentum eigenfunction is this
but it is not normalized, and if we apply the normalization condition which is this
will you get infinity instead of 1?
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Floating Normalization of Experimental Data Sets while Fitting Multiple Models
I have $N$ data sets of unequal cardinality, and I am told we do not treat each data set with a normalization of $1$. Instead we let the the normalization float and fit it as though it were any other ...
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Normalization of vacuum state in field theory
I am doing a calculation of an amplitude in QFT, not an expert in the subject so this may be a trivial question but cannot find the answer.
What is the normalization of the vacuum state of the ...
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Eigenfunction of wave vector [closed]
I am reading some book, where it is said that the eigenfunctions are given by
$$\langle \mathbf{r}|\mathbf{k}\rangle = \frac{1}{\sqrt{\Omega}} \mathrm{e}^{i \mathbf{k} \cdot {\mathbf{r}}}$$
First of ...
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Normalisation of the Gaussian wave packet
I have been trying to solve the question asking for the normalisation of the Gaussian wave packet's probability density given as $$\rho(x)=Ae^{-\lambda(x-a)^2}$$ The $\rho(x)$ is just the probability ...
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Normalization of $U(1)$ gauge fields
In G. W. Moore, “Introduction to Chern-Simons theories.” 2019 TASI School. [Online]. Available: https://www.physics.rutgers.edu/~gmoore/TASI-ChernSimons-StudentNotes.pdf the $U(1)$ gauge field has a ...
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Defined Momentum vs. Defined $k$
In quantum mechanics usually we write the momentum operator $\hat{p}$ as:
$$\hat{p} = \hbar \hat{k}. \tag{1}$$
with of course:
$$\hat{p}|p\rangle = p |p\rangle \tag{2}$$
$$\hat{k}|k\rangle=k|k\rangle \...
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Normalization of momentum eigenstates in QFT
Inspired by a previous question, I'd like to ask about the normalization of one-particle states in QFT.
The most common normalization seems to be the covariant one:
$$ \langle \vec p'|\vec p\rangle = (...
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How the normalization condition implies the following relation?
Using equation 2.35 from Peskin and Schroeder:
$$
|\vec{p}\rangle=\sqrt{2 E_{\vec{p}}} a^{\dagger}_\vec{p} |0\rangle
$$
should lead to
$$
U(\Lambda)|\vec{p}\rangle = |\Lambda \vec{p}\rangle,
$$
where ...
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Effects of a Lorentz boost on the normalization of a probability density (Dirac equation)
My question regards the probability densities of the Dirac equation.
As is well known, the Dirac equation implies a continuity equation
$$
\partial_\mu j^\mu = 0
$$
for $j^\mu = c\overline\psi \gamma^\...
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3
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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 ...
user261609
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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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Normalization of Hamiltonian Eigenfunctions for Free Particle [closed]
I am trying to prove that given
$$\phi_E(x) = \left(\frac{m}{2E}\right)^{1/4} \frac{1}{\sqrt{2 \pi \hbar}} e^{i \sqrt{2mE}x/\hbar}$$
Then,
$$\int dx \phi^*_E \left(x\right) \phi_{E^\prime}(x) = \delta(...
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Glauber Surdarshan $P$ Representation Normalizaion
I am studying Scully and Zubiary's quantum optics book currently, and I ran across their definition of the P representation as:
$$P(\alpha,\alpha^*) = Tr[\rho \delta(\alpha^* - a^\dagger) \delta(\...
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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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Normalization relation of the generators of the Lie-algebra of the Yang-Mills gauge group
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(...
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