14. An electron is bound in a one-dimensional infinite square well potential in the first excited state. The wavelength of the lowest energy single photon that the system can absorb is 438 nm. What is the width of the well?

1. A free electron has the wavefunction p(x, t) = sin(kx – wt) and wave number k = 50nm-1 1.1 Determine the electron's de Broglie wavelength. 1.2 Determine the electron's momentum. 1.3 Determine the electron's kinetic energy. 2. An electron is trapped in an infinite potential well of width 1 cm. For what value of n will electron have an energy of 2 eV? 3. Give the Born interpretation of the wavefunction.

3. Prove the function y (x, y,=) = A Sin( L Sin( -)Sin( :) L, L, x, satisfies the Schrodinger's equation for a quantum dot with a width of Lx, Ly, and Lz, and the particle energies are, n. E, = 2m L L L with n,,n.,n, = 1,2,3,...

4. Consider the two-time position correlation functions, C(t)= (X(t)x(0)), where X(t) is the position operator in the Heisenberg picture. Evaluate this function explicitly for the ground state of a one-dimensional quantum harmonic oscillator.

Let Vx/312 is a nomalized wave function for 0 < x < V6L what is the probability of a particle lies between 0 < x < L? A. 3.3 %. В. 16.6% С. 25.0%. D. 100.0 %. А. В. OD.

2. Taas, Baba A particle of mass m is confined in an infinite well potential. It is initially at some energy state Em and it transitioned back to its ground state emitting a photon with wavelength 365[nm]. If the ground state is E₁ = 1.02[eV], what is the value of Em? Em [eV]

The electron moves in an infinitely deep. potential well with a width of l=0.15 nm. a) Calculate the minimum (i.e. ground state) speed of the electron. V₁=? b) Calculate the reaction force that the electron causes when it moves back and forth and collides with the other wall of the well adiabatically (thermally insulated). F=? c) Calculate the frequency of the electron's back and forth motion. f=?

1. A particle is confined to the x-axis between x = 0 and x = L. The wave function 3π of the particle is = A sin (²x) + A sin (37 x) with A E R. 4 2L a. b. C. Determine A. Determine the probability that the particle is in the interval [0,1]. J Determine (x).

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4. Normalize the following wavefunctions 4 55 (a) v(x) = sin (#2); =sin(); for a particle in a 1D box of length L. (b) (2) = xe-z|2 (c) (x) = e(x²/a²)+(ikz) 5. In a region of space, a particle with mass m and with zero energy has a time- independent wave-function (x) = Ae-2/12, where A and L are constants. Use your knowledge of the Schrödinger equation to determine the potential energy V(x) of the particle. Plot the potential function? What is the minimum potential energy for the particle, if it is an electron and L = 1 fm? Is this potential repulsive or attractive?