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)

Expert Solution

Manojponduru answered 2 years ago

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.)

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...

For a finite potential well, how would you calculate the energy values in which you would...

For a finite potential well, how would you calculate the energy values in which you would have bound states?

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).

calculate the pi-electron energy levels and the total pi-electron energy of bicyclobutadiene. comment on the stability...

calculate the pi-electron energy levels and the total pi-electron energy of bicyclobutadiene. comment on the stability of bicyclobutadiene with respect to cyclobutadiene. go on to solve the secular equations to obtain the orbital coefficients of the 4 molecular orbitals and hence obtain the pi-charge distributions at each of the atoms.

Show that in a parabolic potential well, the spacing between the energy levels is constant. In...

Show that in a parabolic potential well, the spacing between the energy levels is constant. In semiconductors, parabolic potential wells are often produced by using narrow square potential wells where the well to barrier width ratio gradually changes. Use the virtual crystal approximation to design a GaAs/AlAs parabolicwell where the level spacing for the electron is approximately 8meV. (Hint: This isthe harmonic oscillatorproblem.)

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 an electron confined to an infinite well of width 2ao (Bohr radius). Compare its energy...

Consider an electron confined to an infinite well of width 2ao (Bohr radius). Compare its energy in its three lowest energy states to the three lowest energy states of the Bohr model of the hydrogen atom. Repeat for a proton confined to a well of width 2x10-15 m (a nucleus).

An electron is confined by some potential energy well centered about the origin, and is represented...

An electron is confined by some potential energy well centered about the origin, and is represented by the wave function ψ(x) = Axe−x2/L2, where L = 4.48 nm. The electron's total energy is zero. (a) What is the potential energy (in eV) of the electron at x = 0? eV (b) What is the smallest value of x (in nm) for which the potential energy is zero? nm

a) An electron with 10.0 eV kinetic energy hits a 10.1 eV potential energy barrier. Calculate...

a) An electron with 10.0 eV kinetic energy hits a 10.1 eV potential energy barrier. Calculate the penetration depth. b) A 10.0 eV proton encountering a 10.1 eV potential energy barrier has a much smaller penetration depth than the value calculated in (a). Why? c) Give the classical penetration depth for a 10.0 eV particle hitting a 10.1 eV barrier.

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