Quantum Mechanics Answers

Calculate the critical frequency for the E layer if maximum ionic densities are 3 x 10⁶

A.15.58 x 10⁶

B.15.58 kHz

C.1.58 x 10³

D.None of the above

Estimate the velocity of neutrons needed for the study of neutron diffraction of crystal structures 

if the interatomic spacing in the crystal is of the order of 2 Å. Also estimate the kinetic energy 

of the neutrons corresponding to this velocity. Mass of neutron = 1.6749 x 10 -27 kg.

. Derive Schrodinger wave equation from Cartesian coordinates into Spherical polar coordinates. 1 𝑟 2 𝜕 𝜕𝑟 (𝑟 2 𝜕𝜓 𝜕𝑟 ) + 1 𝑟 2𝑠𝑖𝑛𝜃 𝜕 𝜕𝜃 (𝑠𝑖𝑛𝜃 𝜕𝜓 𝜕𝜃) + 1 𝑟 2𝑠𝑖𝑛2𝜃 𝜕 2𝜓 𝜕𝜙2 + 2𝑚 ℏ 2 (𝐸 − 𝑈)𝜓 = 0

In Stern-Gerlach experiment, calculate the force being exerted on the silver atoms due to the inhomogeneous magnetic field and hence calculate the maximum displacement occurs between the traces. 

Consider the wave function 𝜓(𝑥) = 𝐴𝑐𝑜𝑠 𝑘𝑥 where A, k are constants. Is this the eigenstate of the operators 𝐻̂, 𝑝̂, 𝑝̂ 2 of a particle moving in a potential-free region. If so find the eigenvalues.

Solve Second Order (linear and homogenous) Differential Equation 𝑑 2𝑦 𝑑𝑥2 + 𝑝(𝑥) 𝑑𝑦 𝑑𝑥 + 𝑄(𝑥)𝑦 = 0 by writing it in terms of quadratic equation and solving for its roots, mainly the complex roots. 

• let a wave function Ψ(x,t)=N[(1+i)/2 φ1(x)e^(−iE1t/h)+1/2^1/2 φ2(x)e^(−iE2t/h) Is this wave function is solution of shodinger equation?

Compute the expectation value of ,  operators for a pparticle in general state  where A and  are real physics constants,  and  represents the position and momentum operator. What is the value of A in terms of .

what is photon

a)If the work function foe a metal is 1.85 ev, what would be the stopping potential for light having a wavelength of 410 nm? b) what would be the maximum speed of the emitted photoelectrons at the metals surface?