Show TeX
Notices

Documents

For page specific messages
For page specific messages
Enter a comma separated list of user names.
1679 records found.
Operations
Selected 10 rows in this page.  
Title & Summary Author Updatedsort ascending

\(\S\S\) 7.14 Q[5] \(\int_0^\infty \frac{x^3}{e^x-1}=\frac{\pi^4}{15}\)

Summary (or abstract) not available for this node.
kapoor kapoor's picture 28/10/18

\(\S\S\) 7.14 Integrals from Statistical Mechanics

Summary (or abstract) not available for this node.
kapoor kapoor's picture 28/10/18

Problem-QM-20020

Prove that $$ \sigma_j \sigma_k = \delta_{jk} + i\epsilon_{jkl}\sigma_l$$ where \(\sigma_k, k=1,2,3\) are Pauli matrices.

kapoor kapoor's picture 28/10/18

Problem-QM-20019

Show that  a  \( 2\times 2 \) complex matrix, which anticommutes with all the three Pauli matrices, must be null matrix.

kapoor kapoor's picture 28/10/18

Problem-QM-20018

Is it correct to say that the Pauli matrices are
(a) hermitian   (b) unitary  (c)  idempotent   (d)  projection

kapoor kapoor's picture 28/10/18

Problem-QM-20017

If $\vec{\alpha}$ is a vector $(\alpha_1,\alpha_2,\alpha_3)$, show that  $$ (\vec{\alpha}\cdot\vec{\sigma})^2 = |\vec{\alpha}|^2$$  where \(|\alpha|=\sqrt{\alpha_1^2+\alpha_2^2+\alpha_3^2}\)  Use this result and show that \[\exp(i\vec{\alpha}\cdot\vec{\sigma}) =
\cos{|\vec{\alpha}|} + i\vec{\alpha}\cdot\sigma \sin|\vec{\alpha}|\]

kapoor kapoor's picture 28/10/18

Problem-QM-20016

Show that the Pauli matrices anti-commute. $$\sigma_j\sigma_k + \sigma_k\sigma_j  =2\delta_{jk}$$ and that the square of each Pauli matrix is identity matrix. $$\sigma_k^2=I, \qquad k=1,2,3$$

kapoor kapoor's picture 28/10/18

Problem-QM-20013

Show that for a system of two identical particles having spin $s$, the ratio of the number of states, symmetric under exchange of spins, to the number of the antisymmetric states is given by ${(s+1)\over s}.$

kapoor kapoor's picture 28/10/18

QM-20 :: Spin and Identical Particles

Summary (or abstract) not available for this node.
kapoor kapoor's picture 28/10/18

Problem-QM-20015

Prove that the Pauli matrices satisfy the commutation relations.
 $$    [\sigma_i,\sigma_j]=2i\epsilon_{ijk}\sigma_k  $$

kapoor kapoor's picture 28/10/18

Pages