Questions tagged [normalization]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3 votes
0 answers
39 views

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 $t_i$...
Diego Ramil's user avatar
2 votes
1 answer
134 views

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 ...
Yair's user avatar
  • 1,687
1 vote
0 answers
59 views

Meaning of Scattering-Amplitudes "time-volume"

I've been reading this book by Schwichtenberg as I re-learn QFT. My question is general, but applies easiest to the scattering amplitude at first order in the $\phi^4$-theory for $k_1,k_2\rightarrow ...
derEddi's user avatar
  • 11
0 votes
1 answer
109 views

Free particle probability to go from $a$ to $b$ [duplicate]

Feynman and Hibbs write that the probability for a particle to go from $a$ to $b$ is \begin{equation*} P(b,a)=|K(b,a)|^2 \end{equation*} The kernel for a free particle is given as \begin{equation*} K(...
Hey Man's user avatar
  • 150
1 vote
0 answers
70 views

Problematic Factor of 2 in Klein-Gordon Propagator Derivation

I want to derive the Klein-Gordon Green function equation $$(\Box_b + m^2) D_F(x_b - x_a) = - i \delta^4(x_b - x_a)$$ by using the same steps taken when fixing the 'exact' Green function of the non-...
bolbteppa's user avatar
  • 3,866
1 vote
0 answers
76 views

Sublattice Magnetization of Heisenberg Model on triangular lattice

I'm trying to rederive the expressions for the square of the sublattice magnetization of the $120^\circ$ Neel antiferromagnetic (NAFM) and the stripe phase on the triangular lattice as shown in ...
WikawTirso's user avatar
-1 votes
1 answer
33 views

Is unitarity equivalent to linearity plus conservation of the norm?

Unitarity is the condition that the inner product in the Hilbert space is preserved. But if you suppose that the norm of any state is already preserved, then does unitarity follow from linearity? ...
Adam Herbst's user avatar
  • 2,373
1 vote
1 answer
60 views

Expectation Value Definition [closed]

I think I might just not be thinking things completely through here but I've seen the expectation value of a Hermitian operator written in many sources as both $$\langle A \rangle=\frac{\langle\psi|A| ...
d0uble_a_b4ttery's user avatar
0 votes
1 answer
80 views

Normalisation and Dirac's Formulation of the Path Integral

Zee's Quantum Field Theory in a Nutshell (Dirac's Formulation in Chapter 1.2) contains the following passage (in attached image). Can someone please explain where the normalization is used in getting ...
Jake McNaughton's user avatar
0 votes
1 answer
32 views

Two normalization constants for Dirac plain wave function

I stumbled across two different expressions for a Dirac plane wave function, namely $$\psi=\sqrt{\frac{m}{EV}}ue^{-ip\cdot x}$$ and $$\psi=\frac{1}{\sqrt{2EV}}ue^{-ip\cdot x}$$ where $u$ is the Dirac ...
Len's user avatar
  • 141
3 votes
1 answer
117 views

How to normalize the states in the continuous limit?

In quantum field theories we can perform the continuous limit, where we take the limit $V\rightarrow\infty$ for the volume system. In quantum optics, we can start by absorbing a factor $\left(\frac{L}{...
HerpDerpington's user avatar
5 votes
1 answer
145 views

Non-normalizable eigenfunctions

I was reading Shankar's Principles of Quantum Mechanics when on page 65, he starts talking about infinite spaces and operators in them. He introduces an operator $K$, which in the $x$ basis takes the ...
JS30's user avatar
  • 129
0 votes
0 answers
38 views

How should I normalize the histograms for signal vs background study?

I am currently working on a signal vs. background study for some particle physics detector. I am having a hard time understanding how I should normalize the signal/background histograms such that my ...
Ignis Idea's user avatar
1 vote
1 answer
82 views

I don't understand the normalization of a quantum state in quantum machine learning paper

In the paper arXiv:1307.0411 by Seth Lloyd, Masoud Mohseni, Patrick Rebentrost on page 3, line 8, it says: Constructing the $\log_2N$ qubit quantum state $| v \rangle = |\vec{v}|^{-1/2}\vec{v}$ then ...
Fissan's user avatar
  • 19
0 votes
1 answer
54 views

How to normalize the symmetrizer of a qudit state?

Notations : $\mathcal{H}= \mathbb{C}^d \otimes \cdots \otimes \mathbb{C}^d$ where $\mathbb{C}^d$ appears $N$ times. $S(\mathcal{H})$ is the symmetric subspace of $\mathcal{H}$. $(|\epsilon_1\rangle,...
Baloo's user avatar
  • 111
2 votes
0 answers
47 views

Normalizability of thermal density matrix in QFT

Suppose that I have a system described by a quantum field theory with Hamiltonian $H$ and $U(1)$ charge $Q$. The thermal density matrix is then $$ \rho = \frac{1}{Z} e^{-(H-\mu Q)/T},\quad Z=Tr(e^{-(H-...
user105620's user avatar
  • 1,043
2 votes
2 answers
88 views

Why rescale the kinetic term in Wilsonian renormalization?

I have been doing some reading on Wilsonian renormalization and also Effective Field Theories. It's my understanding, and I could be wrong, that part of the process is to continually rescale the ...
Cory's user avatar
  • 123
-1 votes
3 answers
144 views

Why exactly $\langle x' | x \rangle = \delta(x'-x)$? [duplicate]

If the position state $|x\rangle$ is complete and orthonormal I understand that $$\langle x | y \rangle = \delta(x-y).\tag1$$ However, why exactly $$\langle x' | x \rangle = \delta(x'-x)\tag2$$ How do ...
InvisibleParticle's user avatar
0 votes
1 answer
81 views

What happens to the normalization condition if the wave function is non stationary?

The quantum mechanics courses I have taken as of now pretty much only deal with stationary states of the form: $$\psi(x,t) = \psi(x)\exp{\left(-\frac{iE}{\hbar}t\right)} $$ Now, what about situations ...
agaminon's user avatar
  • 1,535
1 vote
0 answers
32 views

Expression of Dirac delta function by integral of exponential function [duplicate]

In many QFT books including Peskin & Schroeder's and M.Schwartz's mention about Fourier transform and representation of Dirac delta function as $\begin{align} &f(x) = \int\frac{d^3p}{(2\pi)^3}...
hwan's user avatar
  • 157
3 votes
2 answers
152 views

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 - ...
RosTT's user avatar
  • 199
0 votes
1 answer
132 views

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 ...
bubucodex's user avatar
  • 213
0 votes
0 answers
22 views

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 ...
bubucodex's user avatar
  • 213
0 votes
1 answer
117 views

How to normalize a wave function for different potential? [closed]

I have 3 different wave functions for 3 different potentials. Basically, this is the intereaction for a diatomic molecule. $$\psi_1(x) = 0, x<0$$ $$\psi_2(x) = C^{ibx} - C^{-ibx}, 0 \le x \le a$$ $$...
happypaticle's user avatar
0 votes
1 answer
41 views

How do you use Boltzmanns distribution law?

Considering a particle in an isothermal atmosphere: $ f \left( h \right) \delta \left( h \right) = A e^{\frac{-m g h}{k T}} \delta \left( h \right)$ where $A$ is the normalisation constant of the pdf. ...
thicccjk's user avatar
3 votes
1 answer
133 views

Wavefunction renormalization $Z_n$ in QM perturbation theory given in J.J. Sakurai's book

I'd been studying introductory quantum mechanics from J.J. Sakurai's Modern Quantum Mechanics, 3rd Edition. I was reading chapter 5, especially about time-independent perturbation theory, non-...
GeorgePhysics's user avatar
2 votes
1 answer
206 views

Peskin and Schroeder's QFT eq. (9.14): Gaussian momentum field integration of phase space path integral

On Peskin and Schroeder's QFT book page 282, the book considered functional quantization of scalar field. First, begin with $$\left\langle\phi_b(\mathbf{x})\left|e^{-i H T}\right| \phi_a(\mathbf{x})\...
Daren's user avatar
  • 1,347
3 votes
1 answer
142 views

Measure of Functional Integral in Path Integral Formulation

I have a question regarding the prefactor $\sqrt{\left(\frac{m}{2\pi i \hbar \Delta t}\right)}$ in $$\left<x'|e^{-iHt}|x\right> = \int D[x] \exp(\frac{i}{\hbar}\int dt' L(x, \dot{x})),$$ where $$...
Neophyte's user avatar
  • 320
2 votes
1 answer
59 views

Why two energies look same in the relativistic normalization?

I'm reading Peskin's QFT textbook. In this book, to make normalization of momentum eigenstate Lorentz invariant, we define momentum eigenket as $$\left| \mathbf{p} \right> = \sqrt{2E_{\mathbf{p}}} ...
김승현's user avatar
-1 votes
1 answer
277 views

What is the difference between Dirac delta function orthogonality and Kronecker delta orthogonality?

In the derivation of Bloch Wave, I encountered a problem. First of all this is the definition of Bloch Wave: $$ \psi_{n\mathbf{k}} (\mathbf{r} ) = e^{i\mathbf{k} \cdot \mathbf{r} } u_{n\mathbf{k}} (\...
Zhao Dazhuang's user avatar
2 votes
0 answers
70 views

(Srednicki) How to obtain the normalization condition for Dirac field?

I'm reading through srednicki's qft and I met a problem. In its section 41, after he make an assumption that the creation operators of free field theory would work comparably in the interacting theory ...
Dzhou's user avatar
  • 95
0 votes
0 answers
24 views

Chemical potential for BE condensate: why the normalization would (uncorrectly) give $\mu> 0$?

Consider a gas of bosons. Let $g(\epsilon)$ be the distribution of energy levels (degeneracy). Consider the following integral $$I(\beta,\mu)=\int{d\epsilon g(\epsilon}) \frac{1}{e^{\beta(\epsilon-\mu)...
Simon's user avatar
  • 1
1 vote
0 answers
115 views

Normalizing the spherical coordinate wavefunction

I try to normalize the following wave function $$\psi=C_{n l} e^{-\rho / 2} L_{1}^{2 l+1} Y_{l m}$$ Using the normalization condition $$ 1 = |C_{nl}|^2 \int_{0}^{\infty} e^{-\rho} \rho^2 \{L_{1}^{2l+1}...
Dayzk's user avatar
  • 33
-1 votes
1 answer
88 views

Normalize the wave function with spherical harmonics [closed]

I have this wave function: $$\Psi=C e^{-\rho / 2} \rho^{l} L_{1}^{3} Y_{l, m} $$ To normalize the function I have tried to express the polynomial in the function as follows. If: $$L_{1}^{3}(x)=(-1)^{1}...
Dayzk's user avatar
  • 33
2 votes
0 answers
103 views

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. ...
user avatar
1 vote
0 answers
235 views

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 ...
Abir Ghosh's user avatar
0 votes
1 answer
509 views

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 ...
Evan Dasami's user avatar
5 votes
2 answers
638 views

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 ...
Марина Marina S's user avatar
0 votes
1 answer
406 views

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-\...
Tihei22's user avatar
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|\...
user avatar
0 votes
1 answer
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 ...
idislikecoding's user avatar
1 vote
3 answers
274 views

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., ...
Numerical Disintegration's user avatar
2 votes
1 answer
100 views

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/...
George Fanaras's user avatar
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 ...
Simplyorange's user avatar
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 ...
physBa's user avatar
  • 161
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 ...
Alex Gower's user avatar
  • 2,492
-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?
Jaime Viegas's user avatar
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/\...
Dr. Ernesto Chinchilla's user avatar
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)+\...
Tan Tixuan's user avatar
0 votes
1 answer
137 views

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 $|\psi\rangle\langle\psi|$ ...
Lory's user avatar
  • 996

1
2 3 4 5
7