Question

A particle is trapped in an infinite potential well. Describe what happens to the particle’s ground-state energy and wave function as the potential walls become finite and get lower and lower until they finally reach zero (U = 0 everywhere).

Answer #1

ground state energy of a particle in an infinite potential well is

when the potential well becomes finite with potential U the ground state energy is

where

is the penetration depth

The wave function extends to a distance of outside the well and decays exponentially. The wave becomes essentially 0 beyond .

as U becomes less and less penetration of the wave beyond the walls increases. The case where U=0 becomes imaginary , this the case where there are no potential walls , the potential well is non-existing and particle is free . This is the case the particle can be anywhere from - to +

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The potential wall at x = L suddenly (i.e., instantaneously) moves
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(a) Let t = 0 be at the instant of the sudden change in the
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(b) If you measure the energy of the particle in the new well,
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(c) Estimate the...

Consider a particle trapped in an infinite square well potential
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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...

For a particle trapped in a one-dimensional infinite square well
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its ground state is in
a) The left third of the box: 0 ≤ ? ≤ ?/3
b) The middle third of the box: ?/3 ≤ ? ≤ 2?/3
c) The right third of the box: 2?/3 ≤ ? ≤ L
After doing parts a), b), and c):
d) Calculate the sum of the probabilities you got for...

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
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(n = 6)? The seventh excited state
(n = 8)?
fifth excited state
eV
seventh excited state
eV

. Describe briefly what is meant by
Free particle
Potential Step
Potential Well
Particle in a box (infinite well)
Particle in a finite Well
Potential Barrier (Particle tunneling through potential
barrier)
Give a physical example of each case. Also describe their energy
levels.

An electron is trapped in a 0.16 nm wide finite square well of
height ?? = 2.0 keV. Estimate at what distance outside the walls of
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Free particle
Potential Step
Potential Well
a) particle in a box (infinite wall)
b) particle in a finite wall
4.Potential Barrier (Particle tunneling through potential
barrier)
Give a physical example of each case. Also describe their energy
levels.

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a) Calculated energy of the 1st excited state.
b) What is the wavelength of the photon emitted between 1st
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c) If the width of the well is doubled to 2L and mass is halved
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d) What is the photon energy emitted from the...

Considera particle in the ground state of an infinite
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4.
An electron is trapped in a one-dimensional infinite potential well
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(1) Find wavefunction ψn(x) under assumption that the
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(3) If the yellow light (580 nm) can excite the elctron from
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