Question

For the infinite square well we studied in class, you are given the following: Ψ(x,0) =...

For the infinite square well we studied in class, you are given the following:

Ψ(x,0) = A(x/a) for 0<x<a/2 and Ψ(x,0) = A(1-x/a) for a/2<x<a and zero elsewhere.

Calculate the probability of measuring a particular energy E_n. Verify that this probability makes sense.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the full time-dependent wavefunctions Ψ(x, t) = ψ(x)φ(t). For the case of an infinite square...
Consider the full time-dependent wavefunctions Ψ(x, t) = ψ(x)φ(t). For the case of an infinite square well in 1D, these were Ψn(x, t) = Sqrt (2/L) sin(nπx/L) e^(−i(En/h)t In general, the probability density |Ψn|2 is time-independent. But suppose instead of being ina fixed energy state, we are in a special state Ψmix(x, t) = √12(Ψ1 − iΨ2). What is the time-dependent part of |Ψmix|2?
A particle is in the ground state of an infinite square well. The potential wall at...
A particle is in the ground state of an infinite square well. The potential wall at x = L suddenly (i.e., instantaneously) moves to x = 3L. such that the well is now three times its original size. (a) Let t = 0 be at the instant of the sudden change in the potential well. What is ψ(x, 0)? (b) If you measure the energy of the particle in the new well, what are the possible energies? (c) Estimate the...
The infinite potential well has zero potential energy between 0 and a, and is infinite elsewhere....
The infinite potential well has zero potential energy between 0 and a, and is infinite elsewhere. a) What are the energy eigenstates of this quantum system, and what are their energies? In the case of a discrete spectrum, explain where the quantization comes from. b) Suppose we take the wavefunction at a given time to be an arbitrary function of x that is symmetric around the center of the well (at x = a/2). Is this a stationary state in...
In this problem we are interested in the time-evolution of the states in the infinite square...
In this problem we are interested in the time-evolution of the states in the infinite square potential well. The time-independent stationary state wave functions are denoted as ψn(x) (n = 1, 2, . . .). (a) We know that the probability distribution for the particle in a stationary state is time-independent. Let us now prepare, at time t = 0, our system in a non-stationary state Ψ(x, 0) = (1/√( 2)) (ψ1(x) + ψ2(x)). Study the time-evolution of the probability...
Consider the wave function at t = 0, ψ(x, 0) = C sin(3πx/2) cos(πx/2) on the...
Consider the wave function at t = 0, ψ(x, 0) = C sin(3πx/2) cos(πx/2) on the interval 0 ≤ x ≤ 1. (1) What is the normalization constant, C? (2) Express ψ(x,0) as a linear combination of the eigenstates of the infinite square well on the interval, 0 < x < 1. (You will only need two terms.) (3) The energies of the eigenstates are En = h̄2π2n2/(2m) for a = 1. What is ψ(x, t)? (4) Compute the expectation...
A particular positron is restricted to one dimension and has a wave function given by ψ(x)=...
A particular positron is restricted to one dimension and has a wave function given by ψ(x)= Ax between x = 0 and x = 1.00 nm, and ψ(x) = 0 elsewhere. Assume the normalization constant A is a positive, real constant. (a) What is the value of A (in nm−3/2)? nm−3/2 (b) What is the probability that the particle will be found between x = 0.290 nm and x = 0.415 nm? P = (c) What is the expectation value...
1. As we increase the quantum number of an electron in a one-dimensional, infinite potential well,...
1. As we increase the quantum number of an electron in a one-dimensional, infinite potential well, what happens to the number of maximum points in the probability density function? It increases. It decreases. It remains the same 2. If an electron is to escape from a one-dimensional, finite well by absorbing a photon, which is true? The photon’s energy must equal the difference between the electron’s initial energy level and the bottom of the nonquantized region. The photon’s energy must...
An electron is in an infinite one-dimensional square well of width L = 0.12 nm. 1)...
An electron is in an infinite one-dimensional square well of width L = 0.12 nm. 1) First, assume that the electron is in the lowest energy eigenstate of the well (the ground state). What is the energy of the electron in eV? E = 2) What is the wavelength that is associated with this eigenstate in nm? λ = 3) What is the probability that the electron is located within the region between x = 0.048 nm and x =...
Given three non-interacting distinguishable in an infinite 1-D square well potential of width a. (a) Determine...
Given three non-interacting distinguishable in an infinite 1-D square well potential of width a. (a) Determine the ground wave function for the system of distinguishing and the energy of this state. (b) Determine the wave function of the first excited state and its energy.
Consider a particle trapped in an infinite square well potential of length L. The energy states...
Consider a particle trapped in an infinite square well potential of length L. The energy states of such a particle are given by the formula: En=n^2ℏ^2π^2 /(2mL^2 ) where m is the mass of the particle. (a)By considering the change in energy of the particle as the length of the well changes calculate the force required to contain the particle. [Hint: dE=Fdx] (b)Consider the case of a hydrogen atom. This can be modeled as an electron trapped in an infinite...