Question

For 1D particle-in-a-box, if a wavefunction corresponds to ground state and 1st excited state: Is the...

For 1D particle-in-a-box, if a wavefunction corresponds to ground state and 1st excited state: Is the wave function an eigenfunction?

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
Find the wave function for the ground state and first two excited states for a particle...
Find the wave function for the ground state and first two excited states for a particle in an infinitely deep square well of width a. Show that the uncertainty relation is satisfied for position and momentum.
The normalized wave functions for the particle is in a 1D box of length L., with...
The normalized wave functions for the particle is in a 1D box of length L., with limits on x = 0 and x = L. V (x) = 0 for 0 <= x <= L and V (x) = Infinity elsewhere. The probability of a particle being between x = 0 and x = L / 8 in the ground quantum state (n = 1) should be calculated.
In class, we are discussing a free particle trapped inside the box. Keeping this discussion in...
In class, we are discussing a free particle trapped inside the box. Keeping this discussion in mind, please answer the following questions. (a) Calculate the probability of finding the particle in the first one third of the box (0 to a/3). The particle is residing in the first excited state. (b) Show that the ground state wavefunction is orthogonal to the first excited state wavefunction. (c) Uncertainty is defined as the square root of variance ( a 2 = -...
5) Unlike the particle in the 1D box and the harmonic oscillator, the energy of the...
5) Unlike the particle in the 1D box and the harmonic oscillator, the energy of the ground state of the 2D rigid rotor is zero. What is the difference between these cases that allows the energy to be zero for the rigid rotor in 2D?
I want you to compare particle in a box with the Bohr atom. For the particle...
I want you to compare particle in a box with the Bohr atom. For the particle in the box you can assume the size is .5x10^-10 m and the particle that is trapped is an electron. For the Bohr atom consider a hydrogen atom. a.) What is the energy of photon emitted when the electron drops from 3->2 and 2->1 in the particle in a box? b.) What is the energy of photon emitted when the electron drops from 3->2...
A particle in an infinite well is in the ground state with an energy of 1.92...
A particle in an infinite well is in the ground state with an energy of 1.92 eV. How much energy must be added to the particle to reach the fifth excited state (n = 6)? The seventh excited state (n = 8)? fifth excited state     eV seventh excited state      eV
a) For a 1D linear harmonic oscillator find the first order corrections to the ground state...
a) For a 1D linear harmonic oscillator find the first order corrections to the ground state due to the Gaussian perturbation. b) Find the first order corrections to the first excited state. Please show all work.
Show that the ground state wavefunction for a 1-D harmonics oscillator is an eigen function of...
Show that the ground state wavefunction for a 1-D harmonics oscillator is an eigen function of harmonic oscillator Hamiltonian operator.
Consider the time-dependent ground state wave function Ψ(x,t ) for a quantum particle confined to an...
Consider the time-dependent ground state wave function Ψ(x,t ) for a quantum particle confined to an impenetrable box. (a) Show that the real and imaginary parts of Ψ(x,t) , separately, can be written as the sum of two travelling waves. (b) Show that the decompositions in part (a) are consistent with your understanding of the classical behavior of a particle in an impenetrable box.
For a particle in a one-dimensional box with the length of 30 Å, its wavefunction is...
For a particle in a one-dimensional box with the length of 30 Å, its wavefunction is ψ1+ψ3. What is the location (except x=0 and x =30 Å) where the probability to find this particle is 0?