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### Problem-QM-20008

If a spin $1/2$ particle has spin pointing along the direction (1,1,1), compute the average values of $S_x,S_y$, and $S_z$. Do you expect to get real values? Why?

kapoor 28/10/18

### Problem-QM-20007

Find the direction along which the spin projection is $1/2$ for a spin  half particle if the spin wave function the particle is given to be

$\chi = \begin{pmatrix} 3\over 5 \\ -{4\over 5} \end{pmatrix}$

kapoor 28/10/18

### Problem-QM-20004

The spin wave function of a spin half particle at time $t=0$ is $$\left( \begin{array}{r} \displaystyle \frac{1}{\sqrt{2}} \\[4mm] \displaystyle {1\over \sqrt{2}}\end{array} \right)$$ and the Hamiltonian is represented by $H =\gamma S_z$. Find

1. the wave function at time $T$,
2. the average value of $S_x$ after time $\pi/3\gamma$

kapoor 28/10/18

### Problem-QM-20003

A particle is in the spin state given by $$\left( \begin{array}{r} \displaystyle{1\over\sqrt{5}}\\[4mm]\displaystyle {-2\over\sqrt{5}} \end{array} \right)$$

1. Compute the ratio of probabilities that the $$S_x$$ has values $$\pm \frac{\hbar}{2}$$
2. Compute the average value of the spin projection in the direction $(1,1,1)$.
kapoor 28/10/18

### Problem-QM-20001

Find the spin wave function for a spin ${1\over2}$ particle. It is  given that spin projection along the $x$- axis has a definite value
(a)$\displaystyle {\hbar\over 2}$                         (b) $\displaystyle -{\hbar\over2}$

kapoor 28/10/18

### Problem-QM-20002

Spin wave function of a spin ${1\over 2}$ particle is given to be $$\vert\phi\rangle = \left( \begin{array}{r} \displaystyle {3\over5} \\ \displaystyle -{4\over 5} \end{array} \right)$$

1. Find the ratio of probabilities that $S_z$ has values $\pm\hbar/2$.
2. Find the ratio of probabilities that $S_x$ has values $\pm\hbar/2$.
3. Compute the average value of spin projection along the direction (1,1,1).

kapoor 28/10/18

### QM-09-11 :: Time Development and Pictures in Quantum Mechanics

Problems and Short Questions on Time Development in QM can be found here.

Follow Navigation Links at the Bottom of the page.

kapoor 27/10/18

### Lectures-SM-05 Grand Canonical Partition Function

Summary (or abstract) not available for this node.
kapoor 27/10/18

### Statistical Mechanics == Home Page == Lecture Notes

Summary (or abstract) not available for this node.
kapoor 27/10/18

### Lectures-SM-05 Thermodynamic Functions in Terms of Grand Canonical Partition Function

Summary (or abstract) not available for this node.
kapoor 27/10/18