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?

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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)

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?

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.

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.

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 a semi-infinite square well: U(x)=0 for 0 ≤ x ≤ L, U(x)=U0 for x >...

Consider a semi-infinite square well: U(x)=0 for 0 ≤ x ≤ L, U(x)=U0 for x > L, and U(x) is infinity otherwise. Determine the wavefunction for E < Uo , as far as possible, and obtain the transcendental equation for the allowable energies E. Find the necessary condition(s) on E for the solution to exist.

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

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