At those turning points, this method uses Airy functions to link approximate solutions in classical and nonclassical regions.
In the Gamow theory of alpha decay, this method is applied to calculate the properties of a toy system with a finite square well potential and a Coulombic 1-over-r tail. This method requires the use of functions whose asymptotic forms for large positive argument z scale as z to the minus one-fourth times an exponential of plus or minus two-thirds times z to the three-halves power. Those functions are solutions to a second-order differential equation that comes up when solving the time-independent Schrodinger equation for a linear potential. This method calculates tunneling probabilities as e to the negative two gamma, where gamma is an integral (*) over position of 1 over hbar times the square root of 2m times E minus V. This approximation uses the "connection formulas" to stitch together solutions to the Schrodinger equation at points where the energy of a bound state is equal to the potential. At those turning points, this method uses Airy functions to link approximate solutions in classical and nonclassical regions. For 10 points, name this triply eponymous approximation that can be used to calculate wavefunctions in scattering problems and for bound states.
In the Gamow theory of alpha decay, this method is applied to calculate the properties of a toy system with a finite square well potential and a Coulombic 1-over-r tail.
WKB approximation [accept Wentzel-Kramers-Brillouin-Jeffreys method or Liouville-Green method]