Questions tagged [normalization]
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379 questions
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Why would the normalisation of a vector with 2 complex numbers only give us 3 real parameters?
If a general spin state is characterised by 2 complex numbers, that would mean that 4 real parameters characterise it. I'm assuming that they are given by the complex and real parts of said complex ...
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Are $S$-matrix elements independent of the quantum field normalization?
In Peskin & Schroeder's book in chapter 12 in the subsection "Alternatives for the Running of Coupling Constants" in the paragraph on QFT's with $\beta(\lambda)=0$ P&S say:
In ...
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Defining a particle count density from the wave function
Given the normalised wave function $\psi_1(r)$ of a single particle, suppose that it is localised inside some region $A$ such that:
$$\int_A d^3r|\psi_1(r)|^2\approx\int d^3r|\psi_1(r)|^2=1$$
Then we ...
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When is it physically justified to normalize the amplitude of an electromagnetic wave to $A = 1$? [closed]
In what contexts is it physically justified to normalize the amplitude of an electromagnetic wave from the full interval (−1…+1), with total amplitude ΔA = 2, to the simplified form A = 1, and to what ...
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What is the conventional place to compensate for a change in Dirac spinor normalization? [closed]
Question
Consider the standard procedure for computing tree-level approximations of cross sections in QED:
Draw the tree-level Feynman diagrams for the process in question.
Convert to diagrams to an ...
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Normalization condition in time independent non-degenerate perturbation theory
I'm trying to understand perturbation theory in quantum mechanics. I'm currently following Cohen-Tannudji's Quantum Mechanics book approach to the subject matter. I'm having troubles deriving second ...
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Why the Expectation Value of a unnormalised state $|\psi\rangle$ is $\langle A\rangle_\psi=\frac{\langle\psi|A|\psi\rangle}{\langle\psi|\psi\rangle}$? [closed]
The typical expectation value formula given most places is
$$\langle A \rangle_\psi = \langle\psi|A|\psi\rangle.$$
this assumes that the state is normalised.
For unnormalised states the formula is
$$\...
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How to implement constraints via delta functions?
I have a question regarding the implementation of constraint equations as delta functions in integrals.
My confusion can best be illustrated with a quick example:
Consider a Gaussian integral of the ...
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Cross section normalization in $2 \to 2$ scattering
Consider Compton scattering $$p_1 + p_2 \to p_3 + p_4$$ in the laboratory frame. According to Quantum Field Theory and the Standard Model by Schwartz, the relation between the differential cross ...
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Is it valid to keep $k_1$ and $k_2$ when considering a light propagating along $z$ axis?
If a mode function of the light is given by $\psi_{\mathbf k}(x^\mu)=ce^{ik_\mu x^\mu}$, where the degrees of freedom of polarization are suppressed, it can be normalized by requiring $\left <\psi_{...
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Magnitude of basisvectors [duplicate]
We know that the inner product of a basis vector of an observable or operator with itself should be 1 and should be 0 when inner producted with any other basis vector of the same observable is $0$.But ...
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Why does this condition hold for normalizable wave functions? [duplicate]
I am reading Griffiths' Introduction to Quantum Mechanics, and on Page 14 the footnote states that in 1D normalizable wave functions $\Psi(x,t)$ goes to zero faster than $\frac{1}{\sqrt{|x|}}$, as |$x$...
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In quantum mechanics, why is the perturbed state orthogonal to the unperturbed state?
In perturbation theory, we may write the full wavefunction as
$$|\Psi\rangle = |\psi^0\rangle + \varepsilon |\psi^1\rangle + \mathcal O(\varepsilon^2).\tag{1}$$
Here I'm focusing on a single energy ...
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Units of wave functions in real and reciprocal space
I'm confused about the units of wave functions in reciprocal space and their Fourier transform in real space. On one hand, I believe the Fourier transform of a reciprocal space wave function in 2D is ...
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Gravitational instantons and normalization
The normalization factor for the gravitational instanton number is commonly stated as $1/384\pi^2$ (see for example Equation (2.27) of Dumitrescu)
$$
\frac{1}{384\pi^2}\int\text{tr}(R\wedge R)\in\...
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