Consider the angular momentum operator Iz in coordinate representation Î₂ = −ih (x2 - y²), a. express Î₂ in spherical coordinates.

3. Prove that angular momentum of a particle confined to the xy palne is quantized 4. Neutrons have no electric charge, so they do not interact with the atomic electrons. Hence, they are very penetrating (e.g.,typically 10 cm in lead). Neutron diffraction was proposed in 1934, to exploit de Broglie's hypothesis about the wave nature of matter. Calculate the momentum and kinetic energy of a neutron whose wavelength is comparable to atomic spacing (1.8×1010 m)

Evaluate the linear momentum and kinetic energy of a free electron described by the wavefunction e-ikx with k = 5 nm-¹

4) Is the function = B sin (bx) an eigenfunction of the operator d/dx = = d/dx if B and b are constants and real numbers? Show your work in detail.