A particle in a 3-dimensional infinite square-well potential has
ground-state energy 4.3 eV. Calculate the energies...
A particle in a 3-dimensional infinite square-well potential has
ground-state energy 4.3 eV. Calculate the energies of the next two
levels. Also indicate the degeneracy of the levels.
A particle in an infinite one-dimensional square well is in the
ground state with an energy of 2.23 eV.
a) If the particle is an electron, what is the size of the
box?
b) How much energy must be added to the particle to reach the
3rd excited state (n = 4)?
c) If the particle is a proton, what is the size of the box? d)
For a proton, how does your answer b) change?
An electron is in the ground state of an infinite square well.
The energy of the ground state is E1 = 1.35
eV.
(a) What wavelength of electromagnetic radiation would be needed
to excite the electron to the n = 4 state?
nm
(b) What is the width of the square well?
nm
Find the energy spectrum of a particle in the infinite square
well, with potential U(x) → ∞ for |x| > L and U(x) = αδ(x) for
|x| < L. Demonstrate that in the limit α ≫ hbar^2/mL, the low
energy part of the spectrum consists of a set of closely-positioned
pairs of energy levels for α > 0. What is the structure of
energy spectrum for α < 0?
For the infinite square-well potential, find the probability
that a particle in its second excited state is in each third of the
one-dimensional box: 0?x?L/3 L/3?x?2L/3 2L/3?x?L There's already an
answer on the site saying that the wavefunction is equal to
?(2/L)sin(2?x/L). My professor gave us this equation, but also gave
us the equation as wavefunction = Asin(kx)+Bcos(kx), for specific
use when solving an infinite potential well. How do I know which
equation to use and when? Thanks
For the infinite square-well potential, find the probability
that a particle in its fifth 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 a particle in an infinite potential well the separation
between energy states increases as n increases (see Eq. 38-13). But
doesn’t the correspondence principle require closer spacing between
states as n increases so as to approach a classical (nonquantized)
situation? Explain.
Find the lowest two "threefold degenerate excited states" of the
three-dimensional infinite square well potential for a cubical
"box." Express your answers in terms of the three quantum numbers
(n1, n2, n3). Express the energy of the two excited degenerate
states that you found as a multiple of the ground state (1,1,1)
energy. Would these degeneracies be "broken" if the box was not
cubical? Explain your answer with an example!
The ground state energy of an oscillating electron is 1.24 eV. How much energy must be added to the electron to move it to the second excited state? The fourth excited state?
Consider a particle in an infinite square well, but instead of
having the well from 0 to L as we have done in the past, it is now
centered at 0 and the walls are at x = −L/2 and x = L/2.
(a) Draw the first four energy eigenstates of this well.
(b) Write the eigenfunctions for each of these eigenstates.
(c) What are the energy eigenvalues for this system?
(d) Can you find a general expression for the...
Calculate the wavefunction and energy levels for the
infinite square well.
Go through the full calculation, using boundary conditions and
normalization. Then,
calculate < x > and < p > for the system.