Highly accurate solutions for the confined hydrogen atom

The model of the confined hydrogen atom (CHA) was developed by Michels et al. 1 in the mid‐1930s to study matter subject to extreme pressure. However, since the eigenvalues cannot be obtained analytically, even the most accurate calculations have yielded little more than 10 figure accuracy. In this work, we show that it is possible to obtain the CHA eigenvalues with extremely high accuracy (up to 100 decimal digits) and we do that using two completely different methods. The first is based on formal solution of the confluent hypergeometric function while the second uses a series method. We also compare radial expectation values obtained by both methods and conclude that the wave functions obtained by these two different approaches are of high quality. In addition, we compute the hyperfine splitting constant, magnetic screening constant, polarizability in the Kirkwood approximation, and pressure as a function of the box radius.