Question

The wave function of a particle is exp(i(kx-omegat)), where x is distance, t is time, and k and co are positive real numbers. The x-component of the momentum of the particle is a. 0 b. h omega c. hk d. t omega/c| e.hk/omega

Answer 1

Answer:

Momentum, $p=\hbar k$

Explanation:

The wave function of a particle is given by :

$y=exp[i(kx-\omega t)]$...............(1)

Where

x is the distance travelled

t is the time taken

k is the propagation constant

$\omega$ is the angular frequency

The relation between the momentum and wavelength is given by :

$p=\dfrac{h}{\lambda}$............(2)

From equation (1),

$k=\dfrac{2\pi}{\lambda}$

$\lambda=\dfrac{2\pi}{k}$

Use above equation in equation (2) as :

$p=\dfrac{h k}{2\pi }$

Since, $\dfrac{h}{2\pi}=\hbar$

$p=\hbar k$

So, the x-component of the momentum of the particle is $\hbar k$. Hence, this is the required solution.