We introduce a simple and practical method to be able to write down almost all the fundamental formulas of thermodynamics. Firstly, we write out in a certain order the four characteristic functions, internal energy U, free energy F, enthalpy H, and Gibbs function G, and the four basic thermodynamic variables, volume V, pressure P, temperature T, and entropy S. Secondly, some rules are specified. According to these rules, the intrinsic independent variables of each characteristic function are clearly revealed; the relationships between the characteristic functions, the partial derivatives of the functions with respect to the intrinsic variables, and the partial derivative relationships between the thermodynamic variables, i.e., Maxwell relations, can be put down. Finally, the pressure and volume are expanded to other intensive and extensive quantities. These rules of memory are actually a summary of the features of the basic formulas of thermodynamics.

This paper solves the eigenvalues of the bound states of the Dirac equation when there is a Coulomb potential in its Hamiltonian. In the literature, only a positive energy spectrum is solved for this Hamiltonian, which is less than the rest energy and describes the bound states. The author calls it positive energy solutions. In this paper, we show that there are negative energy solutions in addition. The positive and negative energy eigenvalues are one-to-one correspondence and just contrary numbers to each other, which is called the symmetry with respect to the positive and negative eigenvalues. The present work shows that the Dirac equation with a Coulomb potential has symmetry of positive and negative eigenenergy values for both the bound states and unbound states.