5. Consider a particle in a two-dimensional, rigid, square box with side a. (a) Find the...

5. Consider a particle in a two-dimensional, rigid, square box with side a. (a) Find the time independent wave function φ(x,y)describing an arbitrary energy eigenstate. (b)What are the energy eigenvalues and the quantum numbers for the three lowest eigenstates? Draw the energy level diagram

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genius_generous answered 1 year ago

Solve the schordingers equation for a particle in a rigid two-dimensional box.

Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions....

Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions. a) Derive the density of states per unit energy, D(ε). b) Find the Fermi wavevector, kF, and the Fermi energy, εF, in terms of the number of electrons N and the area of the box, A=L2 . c) Calculate the density of states at the Fermi energy, D(εF), expressed in terms of N and A. Calculate the heat capacity, CV.

Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions....

Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions. a) Derive the density of states per unit energy, D(ε). b) Find the Fermi wavevector, kF, and the Fermi energy, εF, in terms of the number of electrons N and the area of the box, A=L2 . c) Calculate the density of states at the Fermi energy, D(εF), expressed in terms of N and A. Calculate the heat capacity, CV.

Consider a particle of mass m confined to a one-dimensional box of length L and in...

Consider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction. For a partide in a box the energy is given by En = n2h2/8mL2 and, because the potential energy is zero, all of this energy is kinetic. Use this observation and, without evaluating any integrals, explain why < px2>= n2h2/4L2

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal....

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal. Namely, find the relation between m and n so that < m | n > = 0

Consider a particle of mass m that can move in a one-dimensional box of size L...

Consider a particle of mass m that can move in a one-dimensional box of size L with the edges of the box at x=0 and x = L. The potential is zero inside the box and infinite outside. You may need the following integrals: ∫ 0 1 d y sin ⁡ ( n π y ) 2 = 1 / 2 , for all integer n ∫ 0 1 d y sin ⁡ ( n π y ) 2 y = 1...

For two dimensional particle in a box, how many electrons can we get at most in...

For two dimensional particle in a box, how many electrons can we get at most in the first energy level and why?

Benzene may be regarded as a two-dimensional box of side about 3.5 angstroms and containing six...

Benzene may be regarded as a two-dimensional box of side about 3.5 angstroms and containing six pi electrons. Recall than any state can hold a maximum of two electrons. What wavelength of light would be required to promote an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO)?

A particle in an infinite one-dimensional square well is in the ground state with an energy...

A particle in an infinite one-dimensional square well is in the ground state with an energy of 2.23 eV. a) If the particle is an electron, what is the size of the box? b) How much energy must be added to the particle to reach the 3rd excited state (n = 4)? c) If the particle is a proton, what is the size of the box? d) For a proton, how does your answer b) change?

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to...

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to qualitatively demonstrate that the classical probability distribution (any value of x is equally allowed) is obtained for particles at high temperatures.

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5. Consider a particle in a two-dimensional, rigid, square box with side a. (a) Find the...

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Related Solutions

Solve the schordingers equation for a particle in a rigid two-dimensional box.

Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions....

Consider a two-dimensional electron gas in a square box of side L, with periodic boundary conditions....

Consider a particle of mass m confined to a one-dimensional box of length L and in...

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal....

Consider a particle of mass m that can move in a one-dimensional box of size L...

For two dimensional particle in a box, how many electrons can we get at most in...

Benzene may be regarded as a two-dimensional box of side about 3.5 angstroms and containing six...

A particle in an infinite one-dimensional square well is in the ground state with an energy...

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to...