Show TeX
Notices

Documents

For page specific messages
For page specific messages
Enter a comma separated list of user names.
1747 records found.
Operations
Selected 10 rows in this page.  
Title & Summary Author Updatedsort ascending

Problem/QM-23004

A particle moves in two dimensional circular oscillator potential $$  V(x) = {1\over 2} m \omega^2(x^2+y^2) $$ (a) What are the quantum numbers of the first excited state? Is it degenerate or not?
(b) If a small perturbation $H^\prime =  \lambda xy $ is applied compute the lowest order correction to the energy of the first excited state.     

kapoor kapoor's picture 28/12/18

Problem/QM-23005

Use the first order perturbation theory to compute the correction to the $l=1$ level of $$ H = L^2 + \alpha L_x + \beta L_y $$ taking  $$ H_0=L^2, \qquad \mbox{and} \qquad H^\prime =  \alpha L_x + \beta L_y. $$ Find the corrections to the $l=1$ level using first order perturbation theory.

kapoor kapoor's picture 28/12/18

Problem/QM-23006

Following the steps as in the theoretical treatment of perturbation theory, find eigenvectors and eigenvalues of the matrix
 $$\left[ \begin{array}{rrr}        1&\epsilon& 0 \\         \epsilon & 1&-\epsilon \\          0 & -\epsilon& 2    \end{array}\right] $$ upto the lowest non-vanishing order in $\epsilon$.

kapoor kapoor's picture 28/12/18

Problem/QM-23007

Calculate  $\ell=1$ eigenvalues and eigenvectors to the lowest non vanishing order in perturbation theory taking  $$ H_0= \vec{L}^2 + \gamma L_z$$ as the unperturbed Hamiltonian and    $$ H^\prime = \epsilon (L_xL_y+L_y L_x) $$ as perturbation.

kapoor kapoor's picture 28/12/18

Problem/QM-23008

The unperturbed part and the perturbation part of  Hamiltonian for a system can be written as
\begin{equation}H_0= \begin{pmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 2
\end{pmatrix} \quad H^\prime = \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1
& 0 \end{pmatrix} \end{equation}Find the lowest order nonvanishing corrections to the eigenvalues.

kapoor kapoor's picture 28/12/18

Problem/QM-23009

A spectral spectral line due to a transition from an electronic state \(p\) to an \(s\) state splits into three Zeemnan lines in the presence of a strong magnetic field. At intermediate field strengths find  the number of spectral lines that will be observed for this transition.

kapoor kapoor's picture 28/12/18

Problem/QM-23010

Summary (or abstract) not available for this node.
kapoor kapoor's picture 28/12/18

Problem/QM-23011 Time Independent Perturbation Theory

\(\newcommand{\ket}[1]{\vert#1\rangle}\)
\(\newcommand{\bra}[1]{\langle#1\vert}\)In an orthonormal basis consisting of three elements $\{\ket{1},\ket{2}, \ket{3} \}$, the Hamiltonian of a system is given by \begin{equation} H = \ket{1}\bra{1} + i\epsilon \ket{1}\bra{2} - i\epsilon \ket{2}\bra{1} + 2 \ket{2}\bra{2} + 2\epsilon \ket{2}\bra{3} + 2 \epsilon\ket{3}\bra{2} + \ket{3}\bra{3} \end{equation} Find the eigenvalues and eigenvectors of the total Hamiltonian \(H\) upto first order in \(\epsilon\). [Hint: First construct the matrix representation for $H$ in the given basis.]

kapoor kapoor's picture 28/12/18

Problem/QM-23012

Following the steps as in the theoretical treatment of perturbation theory, find eigenvectors and eigenvalues of the matrix  $$\left[ \begin{array}{rrr}         1&\epsilon& 0 \\         \epsilon & 1 &-\epsilon \\          0 & -\epsilon& 2    \end{array}\right] $$ up to the lowest non-vanishing order in $\epsilon$

kapoor kapoor's picture 28/12/18

Problem/QM-23013

A particle, having charge $q$, moves in harmonic oscillator potential $V(x)={1\over 2} m \omega^2x^2$.  Find the shift in the energy level of  the $\mbox{n}^{\mbox{th}}$ excited state when uniform electric field $E$ is applied. Compute the corrections upto lowest order giving a nonzero value.

kapoor kapoor's picture 28/12/18

Pages