1
vote
0answers
29 views

Change of Basis For Pauli Matrix From Z Diagonal to X Diagonal Basis

I want to find a matrix such that it takes a spin z ket in the z basis, $$ \lvert S_z + \rangle_z $$ and operates on it, giving me a spin z ket in the x basis, $$ U \lvert S_z + \rangle_z = ...
2
votes
0answers
106 views

Help with the inverse of a matrix [closed]

In some paper I have been reading there is a matrix $M_{ij} = g_{ij} + \epsilon_{ijk}y_k$. In the RHS $g$ is the metric of some manifold and $y_i = b_i + v_i$ where $b_{ij} = \epsilon_{ijk} b_k$ and ...
3
votes
1answer
38 views

Kraus operator rank

All quantum operations $\mathcal{E}$ on a system of Hilbert space dimension $\mathcal{d}$ can be generated by an operator-sum representation containing at most $\mathcal{d^2}$ elements. Extending ...
0
votes
1answer
27 views

How long does it take for $25~\text{mC}$ to pass a point if the current is $12.5~\text{mA}$? [closed]

How long does it take for $25~\text{mC}$ to pass a point if the current is $12.5~\text{mA}$? I = 12.5mA Q = 25mC t = ? The formula for this question was: I = Q/t, where I is amps, Q is Coulombs and ...
2
votes
1answer
70 views

Deriving photon propagator

In Peskin & Schroeder's book on page 297 in deriving the photon propagator the authors say that $$\left(-k^2g_{\mu\nu}+(1-\frac{1}{\xi})k_\mu k_\nu\right)D^{\nu\rho}_F(k)=i\delta^\rho_\mu ...
1
vote
2answers
84 views

Idempotent Operators

If $P$ is an idempotent operator, $P^2 = P$ and we have a vector $|\psi\rangle$, $P\neq1$, and the relation $$PL |\psi\rangle = L|\psi\rangle,$$ what conclusions can we draw about $L$, which is a ...
-3
votes
3answers
108 views

Eigenvectors of Pauli $\sigma_x$ matrix

I solve for eigenvectors of Pauli X matrix. I get {1,-1} and {1, 1}. In exercises I solve, there is an answer $\frac{1}{\sqrt{2}} $ * {1,1} and $\frac{1}{\sqrt{2}} $ * {1,-1}. Where does that ...
1
vote
1answer
72 views

Manipulation with braket notation

I am still getting used to the braket notation. Is this manipulation correct? $$ \frac{-\hbar^2}{2m}\int_{-\infty}^{\infty}\frac{\partial^2\phi_n^*}{\partial z^2} \phi\,dz = ...
1
vote
0answers
64 views

How to make a base tranformation for a linear operator in QM? [closed]

I have 2 bases A and B with the following kets: Base A: $|a_1\rangle$ and $|a_2\rangle$ Base B: $|b_1\rangle = \frac{1}{\sqrt2} \cdot(|a_1\rangle + i\cdot|a_2\rangle)$ $|b_2\rangle = ...
0
votes
0answers
77 views

Trouble with proof about operators in QM

I would like to complete the following exercise: Prove that if the operators $P_i$ satisfy $P_i^{\dagger}$ = $P_i$ and $P_i^2$ = $P_i$, then $P_iP_j=0$ for all $i\neq j$. From $P_i^2 = P_i$ I ...
2
votes
1answer
86 views

Characteristic polynomial of a Matrix

In fact, this problem is more likely to be a math problem. When I read a paper(http://arxiv.org/abs/0707.2875), the author includes the characteristic polynomial for a type of matrix $A_k$ with ...
3
votes
1answer
230 views

A tensor product of two spin-1 particles

I'm rather confused, and I was hoping if someone could help me figure out this (probably rather elementary) issue. I have two particles with spin 1, whose state I describe by $m_S$ and $m_I$ ...
3
votes
2answers
184 views

Eigenenergies and eigenkets given the Hamiltonian

For a two level system the Hamiltonian is: $$ H=a(|1\rangle \langle1|-|2\rangle\langle2|+|1\rangle\langle2|+|2\rangle\langle1|) $$ where $a$ is a number with the dimension of an energy. I need to ...
2
votes
3answers
77 views

Diagonalization Of $(\sigma_x+\sigma_y)$

Can this matrix $(\sigma_x\pm\sigma_y)$ be diagonalised? Clearly, if $\sigma_x$ is diagonalized by a similarity transformation $S_1\sigma_x{S_1}^{-1}$, then $\sigma_y$ can't be diagonalized by $S_1$, ...
3
votes
1answer
122 views

Determinant and adjunct of $k-\omega^2m$ in terms of natural frequencies

Given is a mechanical multiple degree of freedom system described by the following matrices and equation: mass matrix ${\bf{m}} = \left[\begin{matrix} m & 0 & 0 \\ 0 & m & 0 \\ 0 ...
3
votes
0answers
148 views

Fock Subspaces and Weight Vectors

This is my first time taking a physics course (I'm a mathematics major), so I'm encountering a lot of new things, which I'm kind of expected to know. In particular, how to work with Bosons. I've got ...
1
vote
2answers
1k views

Applying angular velocity to a rotation matrix

I have a very simple question. In our project we store an object's orientation as a 3x3 matrix which holds the orthonormal base of that object's local space. For instance if the object is aligned with ...
2
votes
3answers
1k views

Spring-mass system with two springs and three masses [closed]

I'm trying to solve a system of springs and masses that is confusing me. First, the balls are all lined up linearly. Secondly, the ball in the middle has a smaller mass $m$ while the first and last ...
2
votes
2answers
519 views

2D - Kinematics - Linkage System using Vector Algebra [closed]

I have this question that I dont know how to solve correctly : My question is, how do I find $V_B$ ? I will find the angular velocities myself, but I want to know the method to get $V_B$ ? I know ...
2
votes
3answers
270 views

Vector space of $\mathbb{C}^4$ and its basis, the Pauli matrices

How do I write an arbitrary $2\times 2$ matrix as a linear combination of the three Pauli Matrices and the $2\times 2$ unit matrix? Any example for the same might help ?
1
vote
1answer
643 views

Dimensional Analysis: Buckingham Pi Theorem Using a Matrix

I have the following problem - which is basically that $\omega = f(g,h,l)$ now the book claims that the two $\pi$ terms as follows $\pi_1 = \omega \sqrt{\frac{l}{g}}$ and $\pi_2 = \frac{h}{l}$. Now we ...
1
vote
3answers
154 views

Question about orthonormal decompositions over unitary operators

I'm teaching myself quantum information theory using Nielson and Chuang's "Quantum Computation and Quantum Information" and I'm at a point in the book where the formalism is starting to make my eyes ...