Question

The wave function of a particle in a one-dimensional box of length L is ψ(x) = A cos (πx/L).

Find the probability function for ψ.

Find P(0.1L < x < 0.3L)

Suppose the length of the box was 0.6 nm and the particle was an electron. Find the uncertainty in the speed of the particle.

Answer #1

The wave function for a particle confined to a one-dimensional
box located between x = 0 and x = L is given by Psi(x) = A sin
(n(pi)x/L) + B cos (n(pi)x/L) . The constants A and B are
determined to be

Recall that |ψ|2dx is the probability of finding the particle
that has normalized wave function ψ(x) in the interval x to x+dx.
Consider a particle in a box with rigid walls at x=0 and x=L. Let
the particle be in the first excited level and use
ψn(x)=2L−−√sinnπxL
For which values of x, if any, in the range from 0 to L is the
probability of finding the particle zero?
For which v alues of x is the probability highest?Express your...

A particle is described by the wave function ψ(x) = b(a2 - x2)
for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are
positive real constants.
(a) Using the normalization condition, find b in terms of a.
(b) What is the probability to find the particle at x = 0.33a in
a small interval of width 0.01a?
(c) What is the probability for the particle to be found...

A particle is described by the wave function ψ(x) = b(a2 - x2)
for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are
positive real constants.
(a) Using the normalization condition, find b in terms of a.
(b) What is the probability to find the particle at x = 0.33a in
a small interval of width 0.01a?
(c) What is the probability for the particle to be found...

A particular positron is restricted to one dimension and has a
wave function given by ψ(x)=
Ax between x = 0 and
x = 1.00 nm, and ψ(x)
= 0 elsewhere. Assume the normalization constant A is a
positive, real constant.
(a) What is the value of A (in nm−3/2)?
nm−3/2
(b) What is the probability that the particle will be found
between x = 0.290 nm and x = 0.415 nm?
P =
(c) What is the expectation value...

a. Suppose that at time ta the state function of a one particle
system is Ψ = (2/πc2)3/4 e(exp [– (x2 + y2 + z2)/c2)] where c = 2
nm. Find the probability that a measurement of the particle’s
position at ta will find the particle in the tiny cubic region with
its center at x = 1.2 nm, y = -1.0 nm, z = 0 and with edges each of
length 0.004 nm. Note that 1 nm = 10-9...

A free particle has the initial wave function Ψ(x, 0) = Ae−ax2
where A and a are real and positive constants. (a) Normalize it.
(b) Find Ψ(x, t). (c) Find |Ψ(x, t)| 2 . Express your result in
terms of the quantity w ≡ p a/ [1 + (2~at/m) 2 ]. At t = 0 plot |Ψ|
2 . Now plot |Ψ| 2 for some very large t. Qualitatively, what
happens to |Ψ| 2 , as time goes on? (d)...

For a particle in a one-dimensional box with the length of 30 Å,
its wavefunction is ψ1+ψ3. What is the
location (except x=0 and x =30 Å) where the probability to find
this particle is 0?

Which of the following statements is true for a particle in a
one dimensional box?
A - The probability density is given by ψ *(x)
ψ(x).
B - The probability density is given by ψ *(x)
ψ(x)dx.
C - The probability density has the same value for all values of
x.
D - The probability density evaluated at a point in the box is
always a real number.
Answer Choices:
1) A and D
2) B and D
3) A...

The normalized wave functions for the particle is in a 1D box of
length L., with limits on x = 0 and x = L. V (x) = 0 for 0 <= x
<= L and V (x) = Infinity elsewhere. The probability of a
particle being between x = 0 and x = L / 8 in the ground quantum
state (n = 1) should be calculated.

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