Question

In: Physics

particle of mass m, which moves freely inside an infinite potential well of length a, is...

particle of mass m, which moves freely inside an infinite potential well of length a, is initially in the state Ψ(x, 0) = r 3 5a sin(3πx/a) + 1 √ 5a sin(5πx/a). (a) Normalize Ψ(x, 0). (b) Find Ψ(x, t). (c) By using the result in (b) calculate < p2 >. (d) Calculate the average energy

Solutions

Expert Solution


Related Solutions

a- Consider an electron that moves freely in metal and a particle moves freely in vacuum....
a- Consider an electron that moves freely in metal and a particle moves freely in vacuum. Briefly explain differences between the energy of these particles. b- Briefly explain the temperature dependent conductivity of metal, semiconductor and insulator. (Please write your answer by asking your self “How and Why change” questions )
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...
An infinite potential well in one dimension for 0 ≤ x ≤ a contains a particle...
An infinite potential well in one dimension for 0 ≤ x ≤ a contains a particle with the wave function ψ = Cx(a − x), where C is the normalization constant. What is the probability wn for the particle to be in the nth eigenstate of the innite potential well? Find approximate numerical values for w1, w2 and w3.
Consider the particle-in-a-box problem in 1D. A particle with mass m is confined to move freely...
Consider the particle-in-a-box problem in 1D. A particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = L. The potential energy function is given as (a) Describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) Solve the Schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, En. (c) What are...
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...
For a particle in an infinite potential well the separation between energy states increases as n...
For a particle in an infinite potential well the separation between energy states increases as n increases (see Eq. 38-13). But doesn’t the correspondence principle require closer spacing between states as n increases so as to approach a classical (nonquantized) situation? Explain.
Find the energy spectrum of a particle in the infinite square well, with potential U(x) →...
Find the energy spectrum of a particle in the infinite square well, with potential U(x) → ∞ for |x| > L and U(x) = αδ(x) for |x| < L. Demonstrate that in the limit α ≫ hbar^2/mL, the low energy part of the spectrum consists of a set of closely-positioned pairs of energy levels for α > 0. What is the structure of energy spectrum for α < 0?
A particle with mass m moves on the surface of a cylinder with radius R. At...
A particle with mass m moves on the surface of a cylinder with radius R. At the same time, the force F = -kr on the particle affects it through the z axis. Using the z-and θ generalized coordinates, find the system's hamitonians. Solve the Hamilton equation after defining the conservative quantities.
For the infinite square-well potential, find the probability that a particle in its second excited state...
For the infinite square-well potential, find the probability that a particle in its second excited state is in each third of the one-dimensional box: 0?x?L/3 L/3?x?2L/3 2L/3?x?L There's already an answer on the site saying that the wavefunction is equal to ?(2/L)sin(2?x/L). My professor gave us this equation, but also gave us the equation as wavefunction = Asin(kx)+Bcos(kx), for specific use when solving an infinite potential well. How do I know which equation to use and when? Thanks
For the infinite square-well potential, find the probability that a particle in its fifth excited state...
For the infinite square-well potential, find the probability that a particle in its fifth excited state is in each third of the one-dimensional box: ----------------(0 ≤ x ≤ L/3) ----------------(L/3 ≤ x ≤ 2L/3) ------------------(2L/3 ≤ x ≤ L)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT