Question

There exists a particle with a mass of m and a total energy that is equal to zero. If its wavefunction is given by psi(x) = D*x*e^(-x^2/b^2), where D and b are constants, find the potential energy and constant D (normalization constant).

Answer #1

7. A particle of mass m is described by the wave function ψ ( x)
= 2a^(3/2)*xe^(−ax) when x ≥ 0
0 when x < 0
(a) (2 pts) Verify that the normalization constant is correct.
(b) (3 pts) Sketch the wavefunction. Is it smooth at x = 0? (c) (2
pts) Find the particle’s most probable position. (d) (3 pts) What
is the probability that the particle would be found in the region
(0, 1/a)? 8. Refer to the...

Particles of mass m are incident from the positive x axis
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is greater than U_0.
A) Sketch the potential energy U(x) for this system.
B) How would the wavelength of a particle change in the x<0
region compared to the x>0 region?...

particle of mass m moves under a
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positive constants.
Find the position of stable
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A particle of mass m moves under a force F = −cx^3 where c is a
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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
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The wave function of a particle is ψ (x) = Ne (-∣x∣ /
a) e (iP₀x / ℏ). Where a and P0 are
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a) Find the normalization constant N?
b) Calculate the probability that the particle is between [-a / 2,
a / 2]?
c) Find the mean momentum and the mean kinetic energy of the
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Consider a wave packet of a particle described by the
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possible).
e) Find the minimum uncertainty...

A particle of mass 3m and total energy E = 7m moves toward a
particle of mass m at rest. What is the total system mass?

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