Chapter 6 Finite Size Scaling in Quantum Mechanics

We present the finite-size scaling approach for the calculations of the critical parameters for quantum systems. As an example of how this approach can be used we calculate critical conditions for stable dipole-bound anions. The approach is general and can be used to calculate critical parameters for any given quantum system. The existence of phase transitions is associated with singularities of the free en-ergy. These singularities occur only in the thermodynamic limit[1, 2]. In statistical mechanics, the finite size scaling method provides a systematic way to extrapolate information obtained from a finite system to the thermodynamic limit[3, 4, 5, 6]