If a particle conned to move in one dimension has wavefunction ψ(x), then the probability of nding it between any two points x1 and x2 is: P(x1, x2) = ˆx2 x1 dx |ψ(x)| 2 Calculate the probability of nding a particle between x1 = 0 and x2 = a/3 for the ground-state of a one-dimensional rigid box of size a. [Hint: the calculation involves an integral of the function sin2 θ. Use the identity 2 sin2 θ = 1 − cos 2θ.]

Step-by-step explanation:

The probability of finding a particle between two points is given by:

Furthermore, the wave function of a nth state is given by:

By replacing we obtain

and by using the relation,

we get for the ground state (n=1):

hope this helps!!

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)