Transmission coefficients of a 1D particle in delta potentials

(See attached file for full problem description) --- 4. A particle of mass m, with energy E>0, is moving in the potential V(x) = g a. Write down the solution of the Schrodinger equation in all three regions (xa) for this situation. Assume that the particle is incident from the left. b. Write down the appropriate continuity conditions at x = +a and x = -a. c. Compute the transmission coefficient. Please express your final answer in terms of p*a/h-bar, where p = , and the constant

Homework #02

Problem #1 Consider the Gaussian Distribution ρ(x)= Ae^(-λ(x-a)^2), where A, a, and λ are positive real constants (Look up any integral needed) [A] Use equation 1= ∫ ρ(x) dx (limits on integral are negative infinity to positive infinity) to determine A. [B] Find , , and σ. [C] Sketch the graph of ρ(x). Problem #2 At time t=0 a particle is represented by the wave function… Ψ (x,0) = {A(x/a), if 0≤x≤a, {A((b-x)/(b-a)), if a≤x≤b, {0, otherwise Where A, a, and b are constants. [A] Normalize Ψ (that is, find A, in terms of “a” and “b”) [B] Sketch Ψ (x,0) as a function of ... click for more

Quantum Physics Questions

(See attached file for full problem description)

Quantum Physics Questions

(See attached file for full problem description)

Calculate the standard deviation of the energy for a particle in a state, which is a superposition of two stationary states with coefficients c1 and c2. Do this calculation in two ways: (i) using the wave function of this state and a standard deviation of quantum mechanical averages, and (ii) using the probabilistic interpretation of the coefficients c1 and c2. Did you get the same results?

Calculate the standard deviation of the energy for a particle in a state, which is a superposition of two stationary states with coefficients c1 and c2. Do this calculation in two ways: (i) using the wave function of this state and a standard deviation of quantum mechanical averages, and (ii) using the probabilistic interpretation of the coefficients c1 and c2. Did you get the same results?