Consider our graphical analysis of the bound states in a finite square well of depth V0...

Consider our graphical analysis of the bound states in a finite square well of depth V₀ and width a. Determine

a) The condition on V₀ and a that there is at most one bound state in the problem.

b) The condition on V₀ and a that there is at most four bound states in the problem.

c) Suppose the potential parameters are such that the third bound state is just barely bound. What can you say about the binding energy of the first and second bound states?

Expert Solution

genius_generous answered 1 year ago

Consider a finite square well, with V = 1.2 eV outside. It holds several energy states,...

Consider a finite square well, with V = 1.2 eV outside. It holds several energy states, but we are only interested in two: E1 = 1.15 eV E2 = 1.1 eV 1) For E = 1.15 eV, what is the decay constant, κ, outside the well in nm-1(i.e., where V = 1.2 eV)? κ = 2) For E = 1.1 eV, what is the decay constant, κ, outside the well in nm-1 (i.e.,) where V = 1.2 eV)? κ =...

An electron is bound to a finite potential well. (a) If the width of the well...

An electron is bound to a finite potential well. (a) If the width of the well is 4 a.u., determine numerically the minimum depth (in a.u.) such that there are four even states. Give the energies of all states including odd ones to at least 3 digits. (b) Repeat the calculation, but now keep the depth of the well at 1 a.u., determine the minimum width (in a.u.)

In 1-D, the finite square well always has at least one bound state, no matter how...

In 1-D, the finite square well always has at least one bound state, no matter how shallow the well is. In 3-D, a finite-depth well doesn't always have a bound state.find bound states

In elementary quantum mechanics, the square well is used to model the behavior of a bound...

In elementary quantum mechanics, the square well is used to model the behavior of a bound particle in which one or more forces (external potentials, interaction with other particles, etc) prevent or restrict its ability to move about. We have seen in class that the solutions to the Schrodinger equation in and around the quantum well result in a series of eigenvector wavefunctions with distinct energy levels. In this assignment, we will use MATLAB to create the system and experiment...

A system of N identical, non-interacting particles are placed in a finite square well of width...

A system of N identical, non-interacting particles are placed in a finite square well of width L and depth V. The relationship between V and L are such that only 2 bound states exist. What is this relationship? Hint: What is the requirement on E for a bound state? For these two bound states, what is the expected energy of the system as a function of temperature? The result only applies when T is low enough so that the probability...

Understanding questions a) Explain the difference between a finite and infinite square well, make sketches. b)...

Understanding questions a) Explain the difference between a finite and infinite square well, make sketches. b) How do you calculate the probability density? c) Give an example of what is possible with Heisenberg’s uncertainty principle that would not be classically allowed. d) What is tunneling

Consider a particle in an infinite square well, but instead of having the well from 0...

Consider a particle in an infinite square well, but instead of having the well from 0 to L as we have done in the past, it is now centered at 0 and the walls are at x = −L/2 and x = L/2. (a) Draw the first four energy eigenstates of this well. (b) Write the eigenfunctions for each of these eigenstates. (c) What are the energy eigenvalues for this system? (d) Can you find a general expression for the...

In particular, our process has a finite number of different possible states, namely: anger, disgust, fear,...

In particular, our process has a finite number of different possible states, namely: anger, disgust, fear, joy, sadness, analytical, confident and tentative. If we assume that this process is stationary and Markovian, there must exists a 9×9 transition matrix A encoding the probabilities in Eq. (1) by: aij=P(Xn = si | Xn-1 = sj) where si, sj are any two of the moods defined above and where n is any point in time. Given dataset for a Markov chain model....

Consider a particle of mass ? in an infinite square well of width ?. Its wave...

Consider a particle of mass ? in an infinite square well of width ?. Its wave function at time t = 0 is a superposition of the third and fourth energy eigenstates as follows: ? (?, 0) = ? 3i?3(?)+ ?4(?) (Find A by normalizing ?(?, 0).) (Find ?(?, ?).) Find energy expectation value, <E> at time ? = 0. You should not need to evaluate any integrals. Is <E> time dependent? Use qualitative reasoning to justify. If you measure...

The choices are: ANOM, Chi-Square analysis, ANOVA, and Regression analysis. Please answer part 2 as well....

The choices are: ANOM, Chi-Square analysis, ANOVA, and Regression analysis. Please answer part 2 as well. 1. Identify two analytical tools used to process data collection. 2. How are they processed through organizational information systems?

Question