A spin half particle is in the state $${S_z} = \frac{{{\hbar ^2}}}{2}.$$  The expectation values of $${S_x},\,S_x^2,\,{S_y},\,S_y^2$$   are given by

A particle is placed in a one-dimensional box of size L along the X-axis, (0 < x < L). Which of the following is true?

If the probability that x lies between x and x + dx is P(x) dx = ae^-ax dx, where 0 < x < $$\infty $$ , a > 0, then the probability that x lies between x₁ and x₂ (x₂ > x₁) is

A Michelson interferometer is illuminated with monochromatic light. When one of the mirrors is moved through a distance of 25.3 μm, 92 fringes pass through the cross-wire. The wavelength of the monochromatic light is

An electron is in a statewith spin wavefunction \[{\phi _s} = \left[ {\begin{array}{*{20}{c}} {\frac{{\sqrt 3 }}{2}} \\ {\frac{1}{2}} \end{array}} \right]\]  in the s_z representation. What is the probability of, finding the z-component of its spin along the $$ - {\bf{\hat Z}}$$  direction?