Question

A particle is confined to the one-dimensional infinite potential
well of width L. If the particle is in the

n=2 state, what is its probability of detection between a) x=0, and
x=L/4; b) x=L/4, and x=3L/4; c) x=3L/4,

and x=L? Hint: You can double check your answer if you calculate
the total probability of the particle being

trapped in the well.

Please answer as soon as possible.

Answer #1

An electron is trapped in an infinite one-dimensional well of
width = L. The ground state energy for this electron is 3.8
eV.
a) Calculated energy of the 1st excited state.
b) What is the wavelength of the photon emitted between 1st
excited state and ground states?
c) If the width of the well is doubled to 2L and mass is halved
to m/2, what is the new 3nd state energy?
d) What is the photon energy emitted from the...

Eight electrons are confined to a two-dimensional infinite
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do not electrically interact with one another. Considering electron
spin and degeneracies of some energy levels, what is the total
energy of the eight-electron system in its ground state, as a
multiple of h^2/(8mL^2 )?

II(20pts). Short Problems
a) The lowest energy of a particle in an infinite one-dimensional
potential well is 4.0 eV. If the width of the well is doubled, what
is its lowest energy?
b) Find the distance of closest approach of a 16.0-Mev alpha
particle incident on a gold foil.
c) The transition from the first excited state to the ground
state in potassium results in the emission of a photon with = 310
nm. If the potassium vapor is...

For the infinite square-well potential, find the probability
that a particle in its third excited state is in each third of the
one-dimensional box:
(0 ≤ x ≤ L/3)
(L/3 ≤ x ≤ 2L/3)
(2L/3 ≤ x ≤ L)

For the infinite square-well potential, find the probability
that a particle in its fourth excited state is in each third of the
one-dimensional box:
a) (0 ≤ x ≤ L/3)
b) (L/3 ≤ x ≤ 2L/3)
c) (2L/3 ≤ x ≤ L)

Consider a spinless particle of mass m, which is
moving in a one-dimensional infinite potential well with walls at x
= 0 and x = a. If and are given in Heisenberg picture, how can we
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An electron is trapped in a one-dimensional infinite well. The
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how do you find the 3rd largest wavelength

A proton, a neutron, and an electron are trapped in identical
one-dimensional infinite potential wells; each particle in its
ground state.
a.) At the center of the wells, is the probability density for
the proton greater than, less than, or equal to that of the
electron? Explain.
b.) At the center of the wells, is the probability density for
the neutron greater than, less than, or equal to that of the
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The wave function for a particle confined to a one-dimensional
box located between x = 0 and x = L is given by Psi(x) = A sin
(n(pi)x/L) + B cos (n(pi)x/L) . The constants A and B are
determined to be

1 - Write the one dimensional, time-independent Schrödinger
Wave Equation (SWE). Using the appropriate potential energy
functions for the following systems, write the complete time
independent SWE for:
(a) a particle confined to a one-dimensional infinite square
well,
(b) a one-dimensional harmonic oscillator,
(c) a particle incident on a step potential, and
(d) a particle incident on a barrier potential of finite width.
2 - Find the normalized wavefunctions and energies for the
systems in 1(a). Use these wavefunctions to...

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