Questions tagged [normalization]
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364 questions
-1votes
1answer
132views
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 ...
4votes
0answers
89views
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) $$ \frac{1}{384\pi^2}\int\text{tr}(R\wedge R)\in\...
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1vote
1answer
106views
Question on the square-integrability of the given wavefunction at origin and infinity
I have this function as a wavefunction of a quantum system: $$\psi(r)=N r^a \exp\left(br^2 + cr+\frac d{r^3}+\frac e{r^2}+\frac f{r}\right)$$ where $r$ is the radial parameter ranging on the interval $...
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-2votes
1answer
45views
Quantum scattering states [duplicate]
While studying about scattering states in quantum mechanics we come up with terms like Transmission coefficient and Reflection coefficient in consequence of Obtaining two solutions for x<0 and x>...
0votes
0answers
39views
Why are there constants in the Lagrangian? [duplicate]
I have a question regarding the constant terms in the lagrangian in field theory. Lets take the electromagnetic action in a vacuum for example: $$ S = \int \left( -\frac{1}{4} F_{\mu\nu} F^{\mu\nu} \...
-1votes
1answer
87views
What function should be used to create wave packet for a particle moving in a constant potential if the energy of the particle is greater than $V_0$? [closed]
I have been trying to solve for a particle under a constant potential $V_0$. Now the the energy states are plane waves and to form a normalizable position state we need to form a superposition of all ...
3votes
1answer
203views
In perturbation theory, are there two or three summation terms in the second-order correction to the eigenfunctions?
Context This question is a narrow one and it is specifically related to non-degenerte, time-independent perturbation theory. In working through [1], Sakurai offers in Eq. (5.1.44) that the second-...
- 734
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Differential cross section in electron-positron annihilation
Suppose we have the annihilation reaction $e^{+}e^{-}\to\mu^{+}\mu^{-}$, with the lepton $\mu^{-}$ being produced into a solid angle. In Peskin&Schroeder's intro to QFT book, they state that it is ...
2votes
0answers
56views
Vacuum Polarisation Graphs Cancellation Theorem
I'm going through Mahan's "Many-Particle Physics", and I'm a bit confused about a theorem that he states about the vacuum polarisation terms cancelling out the terms with disconnected ...
- 465
3votes
1answer
176views
On the definition of the stress tensor in two-dimensional CFTs
I started studying CFT recently. I'm following mostly the yellow book by Di Francesco et al. and the shorter book by Blumenhagen and Plauschinn. I'm currently studying how operator product expansions (...
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6votes
3answers
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Can we no longer predict the behavior of a particle with a definite position?
This might be a really dumb question as I am just learning QM for the first time. Shankar says that physically interesting wavefunctions can be normalized to a unit $L^2$-norm: $$\int_{-\infty}^{\...
0votes
1answer
101views
Deriving the normalization factors of $SU(2)$
In Georgi's book on Lie Algebras in Particle Physics, he makes the following argument to derive the normalization factors of $SU(2)$. Define the raising/lowering operators by $J^\pm = (J_1 \pm i J_2)/\...
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1vote
1answer
110views
Zero-point connected correlator $\langle 1 \rangle_C$ is not 1?
This is so confusing: books are saying that connected correlator is given by $$\langle \phi(x_1) \phi(x_2) ... \phi(x_n) \rangle_C = \left.(-i)^{n-1}\frac{\delta }{\delta J(x_1)} \frac{\delta}{\delta ...
- 336
4votes
2answers
361views
Could probability amplitude for a path equal a complex number whose length is always 1 and whose angle is the action divided by Planck's constant?
I'm reading "Zee A. - Quantum Field Theory, as Simply as Possible", where near beginning of explanation of QFT he gives what appears to be path integral formulation, he states: The ...
- 767
1vote
1answer
144views
Dirac-Delta from Normalization of Continuous Eigenfunctions
I'm following this paper, and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \begin{equation} \langle f_s|f_{s'}\rangle = \int_{0}^{1} \...
