Matter waves.

The formula for wavelength of matter wave is.

w=h/p.

Where 'w' is wavelength 'h' is Planck's constant & 'p' is momentum of a particle.

if my particle under observation is at rest with respect to me ,

(i.e. 'p'=0. 'w' is infinite) and is in motion with respect to some another observer,

(i.e. 'p' & 'w' both finite),then what is the actual wavelength of matter wave associated with

that particle?

The wavelength will depend on the reference frame. In your frame it may be infinity but it may have some finite value in some other reference frame.

Here w being the de Broglie wavelength, is the distance travelled by the information about the particle's presence while the particle travels through its Compton wavelength's distance through space:

Taking x as the given particle's Compton wavelength, the velocity of the particle will be

v/c = x/w ,

c being the velocity of light.

Therefore, w is just the amount of time that a particle spends per unit x of space, expressed in meters:

w/c = time spent by the particle within x meters.

So its phase velocity is c/v = w/x, which means, seconds spent per light-second by the particle. This is therefore dependent on the frame of reference.