An electron is trapped in a region between two infinitely high energy barriers. In the region between the barriers the potential energy of the electron is zero. The normalized wave function of the electron in the region between the walls is ψ(x) = Asin(bx), where A=0.5nm1/2 and b=1.18nm-1. Find the energy of the electron in this state of motion.

= = An electron having total energy E 4.60 eV approaches a rectangular energy barrier with U■5.10 eV and L-950 pm as shown in the figure below. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero. Energy E U 0 i (a) Calculate this probability, which is the transmission coefficient. (Use 9.11 x 10-31 kg for the mass of an electron, 1.055 x 10-34] s for h, and note that there are 1.60 x 10-19 J per eV.) (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.60-eV electron tunneling through the barrier to be one in one million? nm

An electron moving in a box of length ‘a’. If Z1 is the wave function at x1 = a/4 with n=1 and Z2 at x = a/4 for n=2 find Z1/Z2

The expectation value of a function f(x), denoted by (f(x)), is given by (f(x)) = f(x)\(x)|³dx +00 Yn(x) = where (x) is the normalised wave function. A one-dimensional box is on the x-axis in the region of 0 ≤ x ≤ L. The normalised wave functions for a particle in the box are given by -sin -8 Calculate (x) and (x²) for a particle in the nth state. n = 1, 2, 3, ....

In the lab you make a simple harmonic oscillator with a 0.15-kg mass attached to a 12-N/m spring. (a) If the oscillation amplitude is 0.10 m, what is the corresponding quantum number n for the quantum harmonic oscillator? (b) What would be the amplitude of the quantum ground state for this oscillator? (c) What is the energy of a photon emitted when this oscillator makes a transition between adjacent energy levels? Comment on each of your results.

Show that normalizing the particle-in-a-box wave function ψ_n (x)=A sin⁡(nπx/L) gives A=√(2/L).

An electron is in an infinite potential well of width 364 pm, and is in the normalised superposition state Ψ=cos(θ) ψ5-sin(θ) i ψ8. If the value of θ is -1.03 radians, what is the expectation value of energy, in eV, of the electron?