Hydrogen atom in a strong magnetic field

The asymptotic solution for a hydrogen atom in a uniform magnetic field of arbitrary strength is obtained. It is derived in the form of common exponential factor multiplied by a finite power of radius time a power series in two variables, the sine of the cone angle and the inverse of radius, with explicit recurrent relations for the coefficients of the power series. It is proven that there exists only one physically acceptable solution in this form. Combining this solution at some radius R with similar series solution in the form of a power series in the radial variable with coefficient being polynomials in the sine, determines the binding energies and wave functions of bound states. To illustrate the usefulness of this approach, the ground-state binding energy of the magnetic field B=100 (in units of 2.35×10⁹G) has been computed with accuracy in 10^-12 hartree. The precision required is ≈30 decimal digits, while the previous result of the same accuracy obtained by direct numerical summation of the series using simple exponential decay as the boundary conditions at finite radius R has been computed in high-precision arithmetic of ≈280 decimal digits. The accuracy of the binding energies of the excited state evolving from 2s₀ exceeds that of previous calculations.