On page 38 of his book Schroeder suggested the following equation:
hf=mc2......(1)
where h is Planck's constant, f is the frequency of deBroglie's wave for a particle, m is the particle's mass and c is speed of light.
Whereas equation (1) is absurd, it is easy to figure out how Schroeder derived it. He read somewhere about the following correct equations [4]:
1) E=hf.....(2)
and 2) E=mc2......(3)
Equation (2) was originally suggested by Planck (in 1900) for the quantum of energy emitted by a black body. In 1905, Einstein applied that equation to the energy of photons regardless of whether they are emitted, traveling or absorbed by a material. In 1923 de Broglie suggested to expand the application of that equation to all particles, either massless as a photon or having a rest mass m. As to equation (3), it is probably the most widely known equation of science derived by Einstein in 1905 as a part of his special theory of relativity.
In both equations (2) and (3) E denotes energy of a particle. Obviously lacking proper understanding of these two equations, and seeing the same letter E on the left side of both, Schroeder mechanically combined the equations (2) and (3) into one equation (1).
Unfortunately for Schroeder, he obviously did not know that E in equation (2) and E in equation (3), while both denoting the energy of a particle, actually denote two different energies. E in equation (2) denotes the variable energy of a moving particle, related to that particle's momentum. E in equation (3) is a constant for a given particle, which denotes the so-called rest energy. These two types of particle's energy have little to do with each other. The absurdity of Schroeder's equation (1) is immediately obvious when we notice that it equalizes a variable quantity to a constant. Indeed, the frequency f of de Broglie wave for a particle is not a fixed constant but depends on the particle's momentum, i.e. on its velocity.
Schroeder could have easily realized the senselessness of his equation (1) if he thought for a minute what are the values of the quantities in that equation.
Planck's constant equals about h=6.626.10-34 J.s while the speed of light equals c=2.997.108 m/s. Let us apply Schroeder's equation (1), for example, to the electron. The mass of an electron is close to 9.1x10-31kg. Then the right side of equation (1), i.e. the electron's rest energy is about 8.17x10-14 Joule, or about 5.1x105 eV (electron-volt). Hence, if Schroeder's equation (1) were correct, all electrons in the world would always have the same energy of about 5.1x105 eV. To have such level of energy, free electrons must be accelerated by a voltage a little more than half a million volt. Of course, different electrons (as well as any other particles) actually possesses different levels of energy in a wide range rather than all having the same energy of about half a million electron-volt.