Questions tagged [matrix-elements]
Matrix elements are the components, or entries, of a matrix, typically considered in a certain basis.
256 questions
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Hermicity not preserved in Hamiltonian [closed]
My question is in the context of a matrix element in a diatomic molecule. I will rephrase it as well as possible to remove any unnecessary complexity.
I denote the spherical harmonic as $Y_m^l = |m,l\...
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Boundary conditions in the finite element method for the Helium atom
In the following paper, the authors obtain the ground state of the helium atom (-2.9032) using the finite element method. The paper can be downloaded here (https://drive.google.com/file/d/...
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Matrix Element of angular Momentum and Vector Operator
I am reading the book The Theory of Atomic Spectra by E. U. Condon and G. H. Shortley. On page 60, they claim that the matrix element of the operator
$$\sum_{j=1}^3\langle j'm'|J_i J_j T_j|jm\rangle$$
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Why do we use matrix in physics? [closed]
I recently started learning theoretical physics by myself and my book (the theoretical minimum series), and in this book, hessian matrix is used for multivariable function, and i want to know that why ...
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Can the projection in the completness operator be applied multiple times in the integral
I'm trying to rewrite the matrix element $\langle k | V |k' \rangle$ of the potential V in terms of position space using the completeness relation.
I know that the completeness relation in position ...
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Help finding matrix elements for $SU(3)$ tensors
I'm trying to solve the following problem:
Find the matrix elements $\langle u|T_a|v \rangle$ where $T_a$ are the $SU(3)$ generators and $|u\rangle$ and $|v\rangle$ are tensors in the adjoint ...
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Possible errata Landau and Lifshitz in $\S29$ Matrix elements of vectors in Quantum Mechanics Third Edition [closed]
Context
L&L write,
Let $\mathbf{A}$ be some vector physical quantity characterizing a closed system... In the particular case where $\mathbf{A}$ is the radius vector of the particle... we find ...
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Physical interpretation of the matrix element
In perturbation theory, but also in other scenarios the claim is made that the following expression:
$|\langle f|\hat O||i\rangle|^2$ represents the probability amplitude for a transition of the ...
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Meaning of Fourier expansions in Heisenberg's matrix mechanics [closed]
I am trying to figure out the passages Heisenberg followed in developing matrix mechanics as presented in his 1925 Umdeutung paper. In developing the virtual oscillators model, Heisenberg uses the ...
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Construction of a parity operator to apply on a lattice system
I am confused with the correct general form of the parity operator to apply it on a lattice system. I am working with the Bose hubbard model of n-sites 1D and total number of particles is fixed.
I ...
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What subset of the Lorentz group produces a given Weyl spinor?
Let's say I have a unit Weyl spinor $\psi = [\psi_1\ \psi_2]^T$. This has 3 degrees of freedom. Now suppose that this spinor was produced from a reference unit spinor — let's take $[1\ 0]^T$ to be ...
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Confused in David Bohm's *Quantum Theory*
In discussing matrix mechanics Bohm says in chapter 16 of Quantum Theory that the $rm$ element of operator $A$, $a_{rm}$, is given by
$$a_{rm} = \int dx\ \psi^*_r(x)A\psi_m(x) \hspace{1in} (Eqn. ...
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Index notation to matrix notation in supersymmetry
Let us consider the barred sigma matrices defined as $$(\overline{\sigma}^\mu)^{\dot{\alpha}\alpha}:=\epsilon^{\alpha \beta} \epsilon^{\dot{\alpha} \dot{\beta}} (\sigma^\mu)_{\beta \dot{\beta}}. \tag{...
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What is the advantage of using spherical tensor over cartesian tensor?
I am trying to train a machine-learning model to forecast the polarizability of atoms within a molecule. Typically, the tensor is characterised as a Cartesian rank-2 tensor, like this:
$$\alpha= \...
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Rotations of coordinate for differently scaled x and y axes
I have a primitive coordinate system where x and y axis are the basis vectors that are orthogonal. Now the lattice constant along x and y is differnt let us say $a_x$ and $a_y$.
I have a vector $\vec{...
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