The equation for the displacement of a matter wave is given by y = ( x - t m ) , where y is displacement, x is position, t is time, m is mass, and is the reduced Planck's constant. Which of the following physical quantities has the same dimensions as the combination ^2 ?

Step-by-step solution

According to the principle of dimensional homogeneity, the arguments of trigonometric functions must be dimensionless. [ x ] = [M^0L^0T^0] [ ] = [ ] [x] The dimensional formula for Planck's constant is [ ] = [ML^2T⁻¹] . [ ] = [ML^2T⁻¹] [L] = [MLT⁻¹] Similarly, for the second term in the argument: [ t m ] = [M^0L^0T^0] [ ] = [m] [t] = [M] [T] = [MT⁻¹] Now, substituting the dimensions of and to find the dimensions of ^2 : [ ^2 ] = [MLT⁻¹]^2 [MT⁻¹] = [M^2L^2T⁻²] [MT⁻¹] = [ML^2T⁻¹] The dimensional formula [ML^2T⁻¹] cor