Consider a free particle of mass m, moving in one dimension in the positive x direction,

Consider a free particle of mass m, moving in one dimension in the positive x direction, in a quantum energy eigenstate in the lab frame. in this lab frame, the coordinate and time labels are denoted by x and t respectively, and the wavefunction, y (x,t), has wavelength 2. now consider the same quantum state observed from a reference frame moving with velocity v, where the coordinates, (x', t'), are related to the lab frame coordinates by the galilean transformation: x= x - vt and t=t. the wavefunction of the particle, as observed from the moving frame, is ý (x',t'). (a) using de broglie's formula or otherwise, find the relation between the wavelength, a', of the particle in the moving frame, and the wavelength, a, in the lab frame. (b) the wavefunctions y (x,t) and ý (x',t') satisfy the schrodinger equation written down in the lab and moving reference frames, respectively. using the ansatz w(x,t)= * (x – vt,t) where a and b are constants to be determined, find the values of a and b, using the schrodinger equations in the two reference frames.