Question

1, Show that the real and imaginary parts
(**separately**) of the time-dependent ground state
wave function psi(x,t) for a particle confined to an impenetrable
box can be written as a linear combination of two traveling
waves.

2, Show the decomposition in (1) is consistent with the classical behavior of a particle in an impenetrable box.

Answer #1

Consider the time-dependent ground state wave function
Ψ(x,t ) for a quantum particle confined to an
impenetrable box.
(a) Show that the real and imaginary parts of Ψ(x,t) ,
separately, can be written as the sum of two travelling waves.
(b) Show that the decompositions in part (a) are consistent with
your understanding of the classical behavior of a particle in an
impenetrable box.

The ground state of a particle is given by the time‐dependent
wave function
Ψ0(x, t) =
Aeαx^2+iβt
with an energy eigenvalue of E0 =
ħ2α/m
a. Determine the potential in which this particle exists. Does this
potential resemble any that you have seen before?
b. Determine the normalization constant A for this wave
function.
c. Determine the expectation values of x,
x2, p, and
p2.
d. Check the uncertainty principle Δx and Δp. Is
their product consistent with the uncertainty...

Please summarize the below article in approximately 100
words:
Monumental function in British Neolithic burial practices
Ian Kinnes
The high-risk rate of survival for the non-megalithic series of
Neolithic funerary monuments, recently re-emphasized by Piggott
(1973: 34), introduces a further variable into the deductive study
of burial practices. In Britain and Europe the overall distribution
of monumental forms present both lacunae and a marked preponderance
of cairns over earthen mounds which are in ill accord with the
known or predicted...

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