A particle is trapped in a one-dimensional potential with energyeigenfunctions n (r) and corresponding energy eigenvalues En. The wavefunction describing the state is3V(x,0) = 3(x) +1₁(x).Using the wave function above, an inexperienced colleague has calculated thefollowing probabilities: P(E3) = 0.64 and P(E₁) = -0.36. Is their answer reasonable and why? If not, can you offer an explanation of what they didwrong, and give the correct results?

Answered: Image /qna-images/answer/5fe91290-2392-4065-a0d5-5f97f031e7d2.jpg

Answered: A particle is trapped in a…

Similar questions

An electron is trapped in a finite well. How “far” (in eV) is it from being free (that is, no longer trapped inside the well) if the penetration length of its wave function into the classically forbidden region is 1nm? The answer should be 0.038eV
Consider the 1-D asymmetric double-well potential Fix Fas sketched below. V(x) W The probability distribution pix) of a particle in the ground state of this potential is best represented by 1P(x) | P(x) (a) (c) |p(x) x (b) (d) X | P(x)
∆E ∆t ≥ ħTime is a parameter, not an observable. ∆t is some timescale over which the expectation value of an operator changes. For example, an electron's angular momentum in a hydrogen atom decays from 2p to 1s. These decays are relativistic, however the uncertainty principle is still valid, and we can use it to estimate uncertainties. ∆E doesn't change in time, so when an excited state decays to the ground state (infinite lifetime, so no energy uncertainty), the energy uncertainty has to go somewhere. Usually, it’s in the frequency of a photon giving a width (through E = hν) to the transition line in an spectroscopy experiment. The linewidth of the 2p state in 9Be+ is 19.4 MHz. What is its lifetime? (Note: in the relativistic atom–photon system, the Hamiltonian is independent of time and both energy and its uncertainty are conserved.)
In a simple model for a radioactive nucleus, an alpha particle (m = 6.64 * 10-27 kg) is trapped by a square barrier that has width 2.0 fm and height 30.0 MeV. (a) What is the tunneling probability when the alpha particle encounters the barrier if its kinetic energy is 1.0 MeV below the top of the barrier (Fig. )? (b) What is the tunneling probability if the energy of the alpha particle is 10.0 MeV below the top of the barrier?
Suppose that the electron in the Figure, having a total energy E of 5.1 eV, approaches a barrier of height Us=6.8 eV and thickness L= 750 pm. (a) What is the approximate probability that the electron will be transmitted through the barrier, to appear (and be detectable) on the other side of the barrier? Energy Us Electron L
A particle of mass 1.60 x 10-28 kg is confined to a one-dimensional box of length 1.90 x 10-10 m. For n = 1, answer the following. (a) What is the wavelength (in m) of the wave function for the particle? m (b) What is its ground-state energy (in eV)? eV (c) What If? Suppose there is a second box. What would be the length L (in m) for this box if the energy for a particle in the n = 5 state of this box is the same as the ground-state energy found for the first box in part (b)? m (d) What would be the wavelength (in m) of the wave function for the particle in that case? m
We have a free particle in one dimension at a time t = 0, the initial wave function is (x, 0) = Ae-r|æ| where A and r are positive real constants. Calculate the expectation value (p).
Question A6 Consider an infinite square well with V = 0 in the interval -L/2 < x < L/2, and V → ∞ everywhere else. A particle of mass m is in the groundstate of this system, and is known to have a wavefunction and energy given by TX √ = COS and E = π²h² 2mL² The system is then perturbed so that its potential takes the constant value V
(a) Consider the following wave function of Quantum harmonic oscillator: 3 4 V(x, t) = =Vo(x)e¯iEot +. Where, Eo, E, are the energy values corresponding to the ground state and the first excited state. Show that the expectation value of î in this state is periodic in time. What is the period? (b) Consider a quantum harmonic oscillator. The operator â4 is defined by : mw 1 â4 = 2h d: 2ħmw Find the expectation value of Hamiltonian for the state â4,(x). ma 1/4,- x2 and , (x) = - mw ma, x2 [Given ,(x) = () mw1/4 2mw x: 1. πή
The normalised wavefunction for an electron in an infinite 1D potential well of length 89 pm can be written:ψ=(-0.696 ψ2)+(0.245 i ψ9)+(g ψ4). If the state is measured, there are three possible results (i.e. it is in the n=2, 9 or 4 state). What is the probability (in %) that it is in the n=4 state?
Consider an electron in a 2D harmonic trap with force constants kxx = 232 N/m and kyy = 517 N/m. List the energies of the lowest 10 eigenfunctions.
A particle is confined to a one dimensional box with boundaries at x=0 and x-1. The wave function of the particle within the box boundaries is V(x) 2100 (- x + ) and zero V 619 everywhere else. What is the probability of finding the particle between x=0 and x=0.621? Do not enter your final answer as a percentage, but rather a number between 0 and 1. For instance, if you get that the probability is 20%, enter 0.2.

SEE MORE QUESTIONS