Answered: The terms state and energy level are… | bartleby

Related questions

Question

100%

The terms state and energy level are not synonymous in quantum mechanics. For the particle in a cubic box, consider the energy range E < 20h²/8ma². How many states lie in this range? How many energy levels lie in this range?

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

A Quantum system has a ground state with energy E0 = 100meV and a 3-fold degenerate excited state with energy E1 = 100meV . Calculate the probability of finding the system in its groud state when it is at T = 300 K? a) 0.94 b) 0.06 c) 1 d) 0.98
V (x) = 00, V(x) = 0, x<0,x 2 a 0
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. What is the probability to find the electron between x = 0.99nm and x = 1.01nm.
The allowed energies of a quantum system are 0.0 eV, 5.5 eV , and 9.0 eV. What wavelengths appear in the system's emission spectrum? (Express your answers in nanometers in ascending order separated by commas).
Problem 3. Consider the two example systems from quantum mechanics. First, for a particle in a box of length 1 we have the equation h² d²v 2m dx² EV, with boundary conditions (0) = 0 and (1) = 0. Second, the Quantum Harmonic Oscillator (QHO) V = EV h² d² 2m da² +ka²) 1 +kx² 2 (a) Write down the states for both systems. What are their similarities and differences? (b) Write down the energy eigenvalues for both systems. What are their similarities and differences? (c) Plot the first three states of the QHO along with the potential for the system. (d) Explain why you can observe a particle outside of the "classically allowed region". Hint: you can use any state and compute an integral to determine a probability of a particle being in a given region.
A quantum mechanical particle moving in one dimension between impenetrable barriers has energy levels ϵ,4ϵ,9ϵ,...ϵ, 4⁢ϵ, 9⁢ϵ, ... , that is En=ϵn2En=ϵ n2 . Suppose that ϵ=0.035eVϵ⁢ =0.035⁢ eV for a certain such quantum system. What is the probability (as a percent) that such a system will be in its ground state when it is in contact with a reservoir at room temperature? The probability that the system will be in its ground state when it is in contact with a reservoir at room temperature is