Question

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 probabilities of finding the particle to have the ground state energy of the new well and the first excited state energy of the new well. (i.e., Estimate the value of c1 and c2, then find the probabilities.) Graphs will help here. (d) Calculate the probability of finding the particle to have the ground state energy of the new well and the first excited state energy of the new well.

Answer #1

Considera particle in the ground state of an infinite
square well where the left half of the well rises at a linear rate
to a potential of V0in a time τ, and then falls back at a
linear rate in a time τ. What is the probability that the
particle is now in the first excited state?

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

quantum physics:
Considera particle in the ground state of an infinite square well
where the left half of the well rises at a linear rate to a
potential of V0in a time t, and then falls back at a linear rate in
a time t. What is the probability that the particle is now in the
first excited state?

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).

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)

A particle of mass m is in the first excited state (i.e., n = 2)
of an ISW that extends from 0 to a in the usual way. Suddenly, the
well expands by 50%, becoming an ISW that extends from 0 to 3a/2.
At the instant the wall moves, the wavefunction is not altered
(although after the wall moves, the wavefunction will begin to
evolve as dictated by the Schroedinger Equation with a new
potential). Note: Having a suddenly expanding...

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.

Exercise
3. Consider a particle with mass m in a
two-dimensional infinite well of length L, x, y
∈ [0, L]. There is a weak potential in the well
given by
V (x,
y) = V0L2δ(x −
x0)δ(y − y0)
.
Evaluate the first order correction to the energy of the ground
state.
Evaluate the first order corrections to the energy of the first
excited states for x0 =y0 = L/4.
For the first excited states, find the points...

An electron is trapped in an infinite square well potential of
width 3L, which is suddenly compressed to a width of L, without
changing the electron’s energy. After the expansion, the electron
is found in the n=1 state of the narrow well. What was the value of
n for the initial state of the electron in the wider well?

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