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.)

Expert Solution

genius_generous answered 2 years ago

Calculate all of the energy levels for an electron in the finite potential well of width...

Calculate all of the energy levels for an electron in the finite potential well of width a) L = 10 Å, b) L = 50 Å, c) L = 100 Å and L = 1000 Å using the actual mass of an electron for the conduction band of the AlGaAs/GaAs/AlGaAs quantum well. Repeat problem using a) the effective mass of an electron in GaAs (electron effective mass meff = 0.067*mass of an electron)

A particle of mass m is confined to a finite potential energy well of width L....

A particle of mass m is confined to a finite potential energy well of width L. The equations describing the potential are U=U0 x<0 U=0 0 < x < L U=U0 x > L Take a solution to the time-independent Schrodinger equation of energy E (E < U0) to have the form A exp(-k1 x) + B exp(k1 x) x < 0 C cos(-k2 x) + D sin(k2 x) 0 < x < L F exp(-k3 x) + G exp(k3...

Estimate the ground state for an electron confined to a potential well of width 0.200 nm...

Estimate the ground state for an electron confined to a potential well of width 0.200 nm and height 100 eV. What is the effective well width of the (infinite) well? (Hint: Consider an iterative approach to approximate the penetration depth ? by initially assuming E?V).

Consider an electron confined in a one-dimensional infinite potential well having a width of 0.4 nm....

Consider an electron confined in a one-dimensional infinite potential well having a width of 0.4 nm. (a) Calculate the values of three longest wavelength photons emitted by the electron as it transitions between the energy levels inside the well [3 pts.]. (b) When the electron undergoes a transition from the n = 2 to the n = 1 level, what will be its emitted energy and wavelength [2 pts.]. To which region of the electromagnetic spectrum does this wavelength belong?...

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...

The solution for the finite potential well is a combination of sine and cosine functions a...

The solution for the finite potential well is a combination of sine and cosine functions a combination of exponential functions a combination of exponential functions and sine and/or cosine functions a third degree polynomial

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...

A free electron is trapped in an infinite well of width L. a- Give the Schrödinger...

A free electron is trapped in an infinite well of width L. a- Give the Schrödinger equation which describes the movement of the electron. b- Show that Ψ (?) = ???? (nπx/L ) is a solution of this equation c- Show that ? = √2/L d- What is the average position of the electron e- What is the most likely position if n = 3 f- What is the average kinetic energy for n = 3 g- What is the...

An electron is trapped in a square well of unknown width, L. It starts in unknown...

An electron is trapped in a square well of unknown width, L. It starts in unknown energy level, n. When it falls to level n-1 it emits a photon of wavelength λphoton = 2280 nm. When it falls from n-1 to n-2, it emits a photon of wavelength λphoton = 3192 nm. 1) What is the energy of the n to n-1 photon in eV? En to n-1 = 2) What is the energy of the n-1 to n-2 photon...

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

Question