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Lecture by Jocelyn

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kapoor kapoor's picture 28/10/18

\(\S\S\) 7.14 Q[3] \(I_m=\int_{-\infty}^\infty \frac{x^m e^x}{(e^x+1)^2}\)

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kapoor kapoor's picture 28/10/18

\(\S\S\) 7.14 Q[2] \(\int_0^\infty \frac{e^x}{(e^x+1)}=\frac{\pi^2}{6}\)

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kapoor kapoor's picture 28/10/18

\(\S\S\) 7.14 Q[1] \(\int_0^\infty \frac{e^x}{(e^x+1)^2} =\frac{1}{2}\)

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kapoor kapoor's picture 28/10/18

\(\S\S\) 7.14 Q[4] \(J(k) = \int_{-\infty}^\infty \frac{e^{ikx} e^x}{(e^x+1)^2}\)

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kapoor kapoor's picture 28/10/18

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

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kapoor kapoor's picture 28/10/18

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

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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

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