Question

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 and C

4) B and C

Answer #1

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.

For a particle in a one-dimensional box of width a, determine
the probability of finding the particle in the right third of the
box (between ‘2/3 a’ and ‘a’) if the particle is in the ground
state. ( Given: Y(x)= sqrt(2/a) sin(npix/a) )

which system does not have a zero point energy? a. particle in
one dimensional box (b). one dimensional harmonic oscillator. (c)
two particle rigid rotor d) hydrogen atom

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?

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

choose all of the following statements that are correct for a
particle in a one dimensional infinite square
a,)the stationary states refers to eigenstates of any operator
corresponding to physical observable
b)in an isolated system if a particle has well -defined position
at time = 0 the position of the particle is well defined at all
times t>0
c)in an isolated system if an energy eigenstate at time t=0 the
energy of the particle is well defined at all times...

A particle is confined to the one-dimensional infinite potential
well of width L. If the particle is in the
n=2 state, what is its probability of detection between a) x=0, and
x=L/4; b) x=L/4, and x=3L/4; c) x=3L/4,
and x=L? Hint: You can double check your answer if you calculate
the total probability of the particle being
trapped in the well.
Please answer as soon as possible.

Which of the following statements is not true about continuous
probability distributions?
Select one:
a. The probability of any event is the area under the density
curve over the range of values that make up the event.
b. The total area under the density curve must be exactly 1.
c. If X is a continuous random variable taking values
between 0 and 500, then
P(X > 200) = P(X ? 200).
d. There are no disjoint events in continuous probability...

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...

For a particle trapped in a one-dimensional infinite square well
potential of length ?, find the probability that the particle is in
its ground state is in
a) The left third of the box: 0 ≤ ? ≤ ?/3
b) The middle third of the box: ?/3 ≤ ? ≤ 2?/3
c) The right third of the box: 2?/3 ≤ ? ≤ L
After doing parts a), b), and c):
d) Calculate the sum of the probabilities you got for...

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