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# Questions tagged [matrix-elements]

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228 views

### Hermitian Matrix

What is the geometrical significance of the Hermitian matrix? Actually what does the conjugate of the transpose represents. As a determinant if 3 by 3 expresses the volume.
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### PDFs expressed through matrix elements of bi-local operators

Extracted from 'At the frontier of ParticlePhysics, handbook of QCD, volume 2', '...in the physical Bjorken $x$-space formulation, an equivalent definition of PDFs can be given in terms of matrix ...
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### Why is a sum remaining here?

Substituting eqn (5.9) into the time-dependent equation gives $$i\hbar \sum_n \dot c_n(t) |u_n\rangle e^{-iE_nt/\hbar} = \sum_n V(t) |u_n\rangle e^{-iE_nt/\hbar}c_n(t) \tag{5.10}$$ Now take the ...
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### How to incorporate refractive index in transfer matrix method

I need to determine the TE and TM reflections at the interface between a uniaxial crystal and air, using a matrix-based method, such as the TMM. I can do so using the Fresnel equation with ease, but ...
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### Heisenberg Hamiltonian 2-Spin Terms in Matrix Representation

I am stuck on the interpretation/derivation of the 2-spin terms of the quantum Heisenberg model Hamiltonian. In this model, our electrons, with spin up or down, are confined to sites on a lattice. ...
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### How can quantum operators be expressed as a matrices?

I have just started quantum mechanics with Shankar. In my understanding, quantum operators are linear operators in infinite-dimensional Hilbert spaces. Shankar has repeatedly treated quantum ...
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### How an operator is converted to a function? [closed]

$$\langle m|F|n\rangle^*=\langle F(n)|m\rangle$$ How does the operator become a function of state $|n\rangle$?
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### How are matrices used to represent quantities, and what is the meaning of a matrix?

So I'm reading this text on Quantum Mechanics, and it goes through a few chapters that I understand fairly well including probability. But then it says that all quantities, like position and energy ...
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### Levi-Civita tensor

The Kronecker delta can be represented by a two dimensional matrix: \begin{gather} \delta_{ij}=\mathbb{I}= \begin{bmatrix} 1&0&0\\ 0&1&0\\ 0&0&1\\ \end{bmatrix}. \end{gather} ...
298 views

### Using Dirac notation to find matrix representation

I am currently reading Sakuria, and I cannot get my head around how one uses the completeness relation to derive the matrix representations of outer products. In the first chapter he states that an ...
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### How to derive the Schrödinger Equation from Heisenberg's matrix mechanics and vice-versa?

How do you derive the Schrödinger equation (wave mechanics, time dependent state) from Heisenberg's Matrix Mechanics (matrix based, time dependent operators)
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### Proof that elastance matrix is invertible

I was reading this lecture notes from MIT OCW on capacitance . It says $V_i =\sum_j P_{ij}Q_{j}$ where the constants $P_{ij}$ are determined by the geometry of the conductors. This matrix can ...
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### Stiffness matrix issue

Good day All, while trying to solve this exercice I was puzzeld by the solution approach indeed, they use the symmetry of the structure, they have made a cut on the hinge where the force F is applied ...
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### Sign issue with the matrix of rotated elements (stiffness matrix)

Good day All I have a doubt regarding the derivation of the following matrix according to my basic understanding we want to go from the basis u1, v1, u2, v2, to the basis u'1, v'1,u'2 ,v'2, and for ...
109 views

### What is norm of matrix element in Fermi Golden Rule

Fermi Golden Rule says: $\Gamma \propto |M_{ij}|^2$ I know how to get $M_{ij}$, but how do I proceed? How do I take a norm of Hermitian matrix? There is no clear (to me) definition in the internet ...
Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely $$\left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ... 0answers 202 views ### Finding a Lens System Matrix for a Planar Concave Thick Lens How can I go about determining the lens system matrix for a planar concave thick lens? I analyzed that a light ray first enters the lens and refracts, then it goes through the lens, and then it ... 1answer 388 views ### Spin-orbit coupling, magnetic field The Hamiltonian of spin-orbit coupling in an external magnetic field \vec{B} = B\vec{e}_z is given by$$ H = \beta L\cdot S+\frac{\mu_b}{\hbar}(L_z+2S_z)B.$$The ladder operators are$$ L_\pm = L_x \...
I was going through a homework problem which is essentially a math review in a kinematics frame. This group of problems start as follows, Given $a_x$, constant acceleration, and initial conditions, ...