Answer:
Momentum, [tex]p=\hbar k[/tex]
Explanation:
The wave function of a particle is given by :
[tex]y=exp[i(kx-\omega t)][/tex]...............(1)
Where
x is the distance travelled
t is the time taken
k is the propagation constant
[tex]\omega[/tex] is the angular frequency
The relation between the momentum and wavelength is given by :
[tex]p=\dfrac{h}{\lambda}[/tex]............(2)
From equation (1),
[tex]k=\dfrac{2\pi}{\lambda}[/tex]
[tex]\lambda=\dfrac{2\pi}{k}[/tex]
Use above equation in equation (2) as :
[tex]p=\dfrac{h k}{2\pi }[/tex]
Since, [tex]\dfrac{h}{2\pi}=\hbar[/tex]
[tex]p=\hbar k[/tex]
So, the x-component of the momentum of the particle is [tex]\hbar k[/tex]. Hence, this is the required solution.
