Q1: Consider the election in a hydrogen atom to initially be in the state: Y(1= 0) = √ -ROYO + √FR₂X₁ -R32Y₂¹² a) What is the probability of measuring the energy of this state and obtaining E₂? at t=0 but something different at t>0 A. at t=0 but something different at t>0 П C. always √3 B. D. always 3 E. Something else. b) Explain your answer. x

4. An H-atom is in is state. a. What is the probability that the electron is found in sphere given by r ≤ ao b. What is (r) ? c. calculate ().

Physics 1. Derive the expression ε(ω)=1- ωp 2 / ω2 , ωp2 =ne2 /ε0m for the dielectric constant as a function of ω for a free electron gas of number density n.   2. Show clearly that metals are opaque to light for which ω is less than ωp.   3. Calculate the wavelength cutoff for Na metal if the volume of a primitive unit cell in Na is 35×10-30 m3   how to solve this problem?

1. A particle is confined to the x-axis between x = 0 and x = L. The wave function 3π of the particle is = A sin (²x) + A sin (37 x) with A E R. 4 2L a. b. C. Determine A. Determine the probability that the particle is in the interval [0,1]. J Determine (x).