Question

In: Physics

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

Solutions

Expert Solution


Related Solutions

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)
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?
Find the lowest two "threefold degenerate excited states" of the three-dimensional infinite square well potential for...
Find the lowest two "threefold degenerate excited states" of the three-dimensional infinite square well potential for a cubical "box." Express your answers in terms of the three quantum numbers (n1, n2, n3). Express the energy of the two excited degenerate states that you found as a multiple of the ground state (1,1,1) energy. Would these degeneracies be "broken" if the box was not cubical? Explain your answer with an example!
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?
Derive the general wavefunction for a particle in a box (i.e. the infinite square well potential)....
Derive the general wavefunction for a particle in a box (i.e. the infinite square well potential). Go on to normalise it. What energy/energies must the particle have to exist in this box?
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...
A particle in a 3-dimensional infinite square-well potential has ground-state energy 4.3 eV. Calculate the energies...
A particle in a 3-dimensional infinite square-well potential has ground-state energy 4.3 eV. Calculate the energies of the next two levels. Also indicate the degeneracy of the levels.
Consider a particle in an infinite square well, but instead of having the well from 0...
Consider a particle in an infinite square well, but instead of having the well from 0 to L as we have done in the past, it is now centered at 0 and the walls are at x = −L/2 and x = L/2. (a) Draw the first four energy eigenstates of this well. (b) Write the eigenfunctions for each of these eigenstates. (c) What are the energy eigenvalues for this system? (d) Can you find a general expression for the...
An electron is in the ground state of an infinite square well. The energy of the...
An electron is in the ground state of an infinite square well. The energy of the ground state is E1 = 1.35 eV. (a) What wavelength of electromagnetic radiation would be needed to excite the electron to the n = 4 state? nm (b) What is the width of the square well? nm
1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for...
1)Consider a particle that is in the second excited state of the Harmonic oscillator. (Note: for this question and the following, you should rely heavily on the raising and lowering operators. Do not do integrals.) (a) What is the expectation value of position for this particle? (b) What is the expectation value of momentum for this particle? (c) What is ∆x for this particle? 2) Consider a harmonic oscillator potential. (a) If the particle is in the state |ψ1> =...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT