Coulomb problem for a &lt;i&gt;Z&lt;/i&gt;&gt;&lt;i&gt;Z&lt;/i&gt;&lt;sub&gt;cr&lt;/sub&gt;

Kuleshov, Valerii M.; Mur, V. D.; Narozhnyi, Nikolai B.; Fedotov, Aleksandr M.; Lozovik, Yurii E.; Попов, В. С.

doi:10.3367/ufnr.0185.201508d.0845

Cited by 6 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since that time almost all researchers in this area repeated this point of view in their publications. However, recently, there appeared a publication [17] where this conclusion was recognized to be wrong. For us, after a rehabilitation of the electron spectrum in the Coulomb field of a point nucleus, it would be very strange to accept the fact that a removal of the singularity of the Coulomb potential at the origin (after a cutoff) makes a situation with the spectrum not better, but worse.…”

Section: Generalmentioning

confidence: 99%

“…Introducing a new energy variable ε by E = m cos ε, ε = arccos E m ∈ (0, π), we rewrite Eqs. (17) as…”

Section: Solving Radial Equations In Regionmentioning

confidence: 99%

“…, n ∈ N} is sometimes called the supercritical charge (or sometimes critical charge, as in Refs. [15,17]), so that there is an infinite set of supercritical charges of nonclear physical meaning. We cannot agree with such a viewpoint for at least two reasons.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Peculiarities of electron energy spectrum in Coulomb field of super heavy nucleus

Гитман¹,

Ferreira²,

Levin³

et al. 2015

Preprint

View full text Add to dashboard Cite

Just after the Dirac equation was established, a number of physicists tried to comment on and solve the spectral problem for the Dirac Hamiltonian with the Coulomb field of arbitrarily large charge Z, especially with Z that is more than the critical value Zc = α −1 ≃ 137, 04, making sometimes contradictory conclusions and presenting doubtful solutions. It seems that there is no consesus on this problem up until now and especially on the way of using corresponding solutions of the Dirac equation in calculating physical processes. That is why in the present article, we turn once again to discussing peculiarities of electron energy spectrum in the Coulomb field of superheavy nucleus. In the beginning, we remind the reader of a long story with a wrong interpretation of the problem in the case of a point nucleus and its present correct solution. We then turn to the spectral problem in the case of a regularized Coulomb field. Under a specific regularization, we derive an exact spectrum equation determining the point spectrum in the energy interval (−m, m) and present some of its numerical solutions. We also derive an exact equation for charges Z providing bound states with energy E = −m. Its analytical and numerical analysis shows that there exists an infinite number of such charges; in this connection , we discuss the notion of supercritical charge.To our mind, their existence does not mean that the one-particle relativistic quantum mechanics based on the Dirac Hamiltonian with the Coulomb field of such charges is mathematically inconsistent. In any case, it is physically unacceptable because the spectrum of the Hamiltonian is unbounded from below, which requires the secondary Fermi-Dirac quantization and transition to many-particle quantum field theory. The consequences of the existence of such charges for quantum electrodynamics with the corresponding Coulomb field remain to be established in the process of constructing such a theory.

show abstract

Section: Generalmentioning

confidence: 99%

“…Introducing a new energy variable ε by E = m cos ε, ε = arccos E m ∈ (0, π), we rewrite Eqs. (17) as…”

Section: Solving Radial Equations In Regionmentioning

confidence: 99%