Question

Given three non-interacting distinguishable in an infinite 1-D
square well potential of width a.

(a) Determine the ground wave function for the system of
distinguishing and the energy of this state.

(b) Determine the wave function of the first excited state and
its energy.

Answer #1

4. Write down the time-independent Schrӧdinger Equation for two
non-interacting identical particles in the infinite square well.
Assuming the spins of the two particles are parallel to each other,
i.e., all spin-up, find the normalized wave function representing
the ground state of the two-particle system and the energies for
the two cases:
(a) Two particles are identical bosons.
(b) Two particles are identical fermions.
and
(c) Find the wave functions and energies for the first and
second excited states for...

For a system composed of two non-interacting, distinguishable
particles of mass m1 and m2
(<<m1) in an 1-D infinite potential well (V=0 for
0<x<a, V=infinite otherwise),
1)Write down the hamiltonian of the system. Obtain the
eigenenergies and eigenfunctions of the hamiltonian by solving the
Hamiltonian eigenequation?
2) For the second-lowest eigenenergy state, what is the
probability to find particle 2 between 0< x < a/4

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...

Show that the wave function of a particle in the infinite square
well of width a returns to its original form after a quantum
revival time T = 4ma^2/π(hbar)

An electron is in the ground state of an infinite square well.
The energy of the ground state is E1 = 1.13 eV.
(a) What wavelength of electromagnetic radiation would be needed
to excite the electron to the n = 7 state? nm
(b) What is the width of the square well? nm

Suppose that an electron trapped in a one-dimensional infinite
well of width 0.341 nm is excited from its first excited state to
the state with n = 5.
1 What energy must be transferred to the electron for this
quantum jump?
2 The electron then de-excites back to its ground state by
emitting light. In the various possible ways it can do this, what
is the shortest wavelengths that can be emitted?
3 What is the second shortest?
4 What...

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?

Consider 3 identical bosons in a one dimensional infinitely deep
well of width 2a.
A.) What is the wave function of the ground state?
B.) What is the wave function of the first excited state?

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?

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)

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