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[MOB/QM-08002]

Node id: 4897page
 AK-47's picture 22-03-07 09:03:23 y

[QUE/QM-23020]

Node id: 4877page

To the lowest non vanishing order in \(\epsilon\), compute the corrections to the
energy levels of the Hamiltonian
\begin{equation}
 H = H_0  + H^\prime
\end{equation}
for the case of spin 1, where
\begin{equation}
   H_0= \vec{S}^2 + S_z^2, \qquad H^\prime = \epsilon S_x
\end{equation}

 AK-47's picture 22-03-05 08:03:46 n

[NOTES/QM-20007] A First Look at the He Atom Energy Levels

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qm-lec-20007

 AK-47's picture 22-03-05 08:03:03 y

[NOTES/QM-20006] Symmetrization Postulate

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qm-lec-20006

 AK-47's picture 22-03-05 08:03:00 y

[NOTES/QM-20005] Identical Particles in Quantum Mechanics

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qm-lec-20005

 AK-47's picture 22-03-05 08:03:58 y

[NOTES/QM-20004] Symmetrization Postulate

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qm-lec-20004

 AK-47's picture 22-03-05 08:03:09 y

[NOTES/QM-20003] Spin Wave Function

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qm-lec-20003

 AK-47's picture 22-03-05 08:03:48 y

[NOTES/QM-20002] Spin Wave Function and Spin Operators

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qm-lec-20002

 AK-47's picture 22-03-05 08:03:56 y

[NOTES/QM-20001] Spin as a Dynamical Variable

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qm-lec-20001

 AK-47's picture 22-03-05 08:03:38 y

[NOTES/QM-18011] Green Function for Perturbative Solution of Scattering

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qm-lec-18011

 AK-47's picture 22-03-04 22:03:06 y

[NOTES/QM-18007] Validity of Born Approximation Square Well Potential

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qm-lec-18007

 AK-47's picture 22-03-04 22:03:04 y

[NOTES/QM-18004] Integral Equation for Scattering

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qm-lec-18004
Some algebraic manipulations
Large r expansion of the formal solution

 AK-47's picture 22-03-04 22:03:02 y

[NOTES/QM-18003] Green Function for Poisson Equation

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qm-lec-18003

 AK-47's picture 22-03-04 22:03:35 y

[NOTES/QM-18002] Perturbative Solution of Differential equation

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qm-lec-18002

 AK-47's picture 22-03-04 22:03:27 y

[NOTES/QM-17009] Addition of Angular Momenta Using Tables

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qm-lec-17009

 AK-47's picture 22-03-04 09:03:02 y

[NOTES/QM-17007] Summary of main results on addition of angular momenta

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qm-lec-17007

 AK-47's picture 22-03-04 09:03:42 y

[NOTES/QM-17005] States Using Ladder Operators

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qm-lec-17005

 AK-47's picture 22-03-04 09:03:06 y

[NOTES/QM-17004] Recurrence Relations for CG Coefficients

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qm-lec-17004

 AK-47's picture 22-03-04 09:03:38 y

[NOTES/QM-17003] Some Useful Restrictions on CG coefficients

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qm-lec-17003

 AK-47's picture 22-03-04 09:03:10 y

[QUE/SM-04004]

Node id: 3237page

The canonical partition function of a system is given by \hfill \HighLight{\fbox{\tiny KPN}} \begin{eqnarray*} Q(T,V,N) &=& \frac{V^N}{N!}\frac{1}{\Lambda^{3N}}\ ;\ \Lambda = \frac{h}{\sqrt{2\pi mk_BT}}. \end{eqnarray*}

  1. Derive an expression for entropy : $S(T,V,N)$.
  2. Consider a quasi-static reversible process in which entropy does not change and $N$ does not change; volume and temperature, however, can change. Show that $TV^{2/3}$ is a constant during such a process.

 

 kapoor's picture 22-03-04 07:03:22 n

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