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

Momentum,
`p=\hbar k`

Step-by-step 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=(h)/(\lambda)`............(2)

From equation (1),

`k=(2\pi)/(\lambda)`

`\lambda=(2\pi)/(k)`

Use above equation in equation (2) as :

`p=(h k)/(2\pi )`

Since,
`(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.