Consider two non-interacting particles in an infinite square well. One is in a state ψm, the...

Consider two non-interacting particles in an infinite square well. One is in a state ψ_m, the other in a state ψ_n with n≠m. Let’s assume that ψ_m and ψ_n are the ground state and 1^st excited state respectively and that the two particles are identical fermions. The well is of width 1Å. What is the probability of finding a particle in the 1^st excited state in a region of width 0.01Å? Does this change if the particles are distinguishable?

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A system of N identical, non-interacting particles are placed in a finite square well of width...

A system of N identical, non-interacting particles are placed in a finite square well of width L and depth V. The relationship between V and L are such that only 2 bound states exist. What is this relationship? Hint: What is the requirement on E for a bound state? For these two bound states, what is the expected energy of the system as a function of temperature? The result only applies when T is low enough so that the probability...

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?

Consider a system of N particles in an infinite square well fro, x=0 to x=N*a. find...

Consider a system of N particles in an infinite square well fro, x=0 to x=N*a. find the ground state wave function and ground state energy for A. fermions. B. bosons.

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

Consider a system of three non-interacting particles confined by a one-dimensional harmonic oscillator potential and in...

Consider a system of three non-interacting particles confined by a one-dimensional harmonic oscillator potential and in thermal equilibrium with a total energy of 7/2 ħw. (a) what are the possible occupation numbers for this system if the particles are bosons. (b) what is the most probable energy for a boson picked at random from this system.

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...

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...

Work out the problem of the infinite square well in two dimensions. In this case, the...

Work out the problem of the infinite square well in two dimensions. In this case, the potential is zero inside a square of sides of length L, and infinite outside the square. Find the eigenfunctions and energy eigenvalues.

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)

Subjects