Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
Sum and Product Puzzle "X" + "Y" and P knows the product "X" × "Y". Both S and P know all the information in this paragraph. The following conversation occurs: What are "X" and "Y"? The solution has "X" and "Y" as 4 and 13, with P initially knowing the product is 52 and S knowing the sum is 17. Initially P does not know the solution, since and S knows that P does not know the solution since all the possible sums to 17 within the constraints produce similarly ambiguous products. However, each can work out the solution by eliminating other possibilities following