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!

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genius_generous answered 1 year ago

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)

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 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?

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.

(a) Prove that there are no degenerate bound states in an infinite (−∞ < x <...

(a) Prove that there are no degenerate bound states in an infinite (−∞ < x < ∞) one-dimensional space. That is, if ψ1(x) and ψ2(x) are two bound-state solutions of − (h^2/2m) (d^2ψ dx^2) + V (x)ψ = Eψ for the same energy E, it will necessarily follow that ψ2 = Cψ1, where C is just a constant (linear dependence). Bound-state solutions should of course vanish at x → ±∞. (b) Imagine now that our particle is restricted to move...

*One dimensional infinite potential well - probability at a location An electron moving in a one-...

*One dimensional infinite potential well - probability at a location An electron moving in a one- dimensional infinite square well of width L is trapped in the n = 1 state. Compute the probability of finding the electron within the "volume" ?x = 0.019 L at 0.55 L to three decimal places.

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?

i. A two-level system has a ground level with four degenerate states and an excited level...

i. A two-level system has a ground level with four degenerate states and an excited level with two degenerate states at 450 cm−1 above the ground level. Please plot the ratio of the number of particles occupying the excited level to the number of particles occupying the ground level as function of temperature (Make sure that the end points and curvature are accurate but anything else can be qualitative). How do i need more Info? This is all given to...

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?...

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