Question

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 calculate the probability of locating particle within a given region.

3 - Setup the wavefunctions in the different regions for 1(c) (for E > U and E < U) and 1(d) (for E < U).

Answer #2

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E>U

answered by: anonymous

Which of the following systems is degenerate?
Question 4 options:
a)
Two-dimensional harmonic oscillator
b)
One-dimensional Infinite square well
c)
One-dimensional finite square well
d)
One-dimensional harmonic oscillator
e)
All time-dependent systems

Consider the 1D Schrodinger's equation independent of
time for the energies E at the interval [0,U] (U>0) of a
particle of mass m at a finite potential wall V(x)=U, 0, U,
respectively x<0, 0<x<L and x>L.
a) The energy espectrum E is continuous or discreet?
Why?
b) Write the general form of the function waves at the 3
regions.
c) Write the equation whose solution gives the energy espectrum.
It's not necessary to solve them.
d) What happen with the...

4.
An electron is trapped in a one-dimensional infinite potential well
of width L.
(1) Find wavefunction ψn(x) under assumption that the
wavefunction in 1 dimensional box whose potential energy U is 0 (0≤
z ≤L) is normalized
(2) Find eighenvalue En of electron
(3) If the yellow light (580 nm) can excite the elctron from
n=1 to n=2 state, what is the width (L) of petential well?

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...

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...

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