Question

An electron has a wavefunction given by 4(x) = A (aeikia + beikar), where =

• a = 5.00 +0.600i
• b= 1.50ein/4 Part 1 If we measure the momentum of the electron, what is the probability that we find p=ħkı?
(a) 0.0815
(b) 0.919
(C) 25.4
(d) 0.916
(e) 0.892

Answer 1

The probability of finding the momentum of the electron as p=ħk is approximately 0.0815.

Step-by-step explanation:

To find the probability of finding the momentum of the electron as p=ħk, we need to determine the coefficients A, a, and b. The probability is given by the square of the wavefunction at that momentum value, which can be calculated by substituting the given values of A, a, b, and k into the wavefunction:

4(x) = A(aeikx + be-ikx)

Once the wavefunction is calculated, we can determine the probability by squaring the wavefunction at p=ħk and multiplying by the infinitesimal volume element:

P(p=ħk) = |4(x)|² * dV

Substituting the wavefunction into the equation and solving for the probability, we find that the probability is approximately 0.0815.