If $$\sigma $$ is the total cross-section and f(θ), θ being the angle of scattering, is the scattering amplitude for a quantum mechanical elastic scattering by a spherically symmetric potential, then which of the following is true? Note that k is the magnitude of the wave vector along the $${{\bf{\hat z}}}$$ direction.
A. $$\sigma = {\left| {f\left( \theta \right)} \right|^2}$$
B. $$\sigma = \frac{{4\pi }}{k}{\left| {f\left( {\theta = 0} \right)} \right|^2}$$
C. $$\sigma = \frac{{4\pi }}{k} \times {\text{Imaginary part of }}{\left| {f\left( {\theta = 0} \right)} \right|^2}$$
D. $$\sigma = \frac{{4\pi }}{k}{\left| {f\left( \theta \right)} \right|^2}$$
Answer: Option C
This Question Belongs to Engineering Physics >> Quantum Mechanics
A. In the ground state, the probability of finding the particle in the interval $$\left( {\frac{L}{4},\,\frac{{3L}}{4}} \right)$$ is half
B. In the first excited state, the probability of finding the particle in the interval $$\left( {\frac{L}{4},\,\frac{{3L}}{4}} \right)$$ is half This also holds for states with n = 4, 6, 8, . . . .
C. For an arbitrary state $$\left| \psi \right\rangle ,$$ the probability of finding the particle in the left half of the well is half
D. In the ground state, the particle has a definite momentum
A. (e-ax1 - e-ax2)
B. a(e-ax1 - e-ax2)
C. e-ax2 (e-ax1 - e-ax2)
D. None of the above
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