The Russians demonstratively taught the Americans (Susskind) about superconductivity and the mechanism of BH and its structure. Maldecena, Kitaev and others, whose names lie behind the scene. A lots of phase transition like fermion to bosonic 2e are not carefully explained. The Hawking radiation from the horizon and originating in the quark-gluon soup (mass of the BH) goes through phase transition and phase space transition, the intricacies of which need to be explained quantum mechanically. However, how SC leads to huge spin of BH (motor action using high superconducting current, generating angular momentum) or how the universe seem like a holograph (information pasted on the wall) remains to be explained.
So what your saying is, the probability for an electron to jump to n+1 energy state, requires almost logarithmically more energy as the energy state approaches the jump
Not true or correct! The probability of an electron transitioning to a higher energy state depends on the specific energy levels involved and the transition rules governed by quantum mechanics. In quantum mechanics, electron transitions between energy levels are typically governed by the absorption or emission of photons. The energy difference between two energy levels determines the energy of the photon required for the transition. The probability of a transition depends on factors such as the selection rules, which govern the allowed transitions based on the quantum numbers of the electron and the initial and final energy states. The energy difference between successive energy levels in a given system can vary, and it is not inherently logarithmic. The energy spacing between energy levels can be different depending on the specific system, such as atoms, molecules, or solid-state materials. Therefore, it is not accurate to make a general statement about the probability requiring logarithmically more energy as the energy state approaches the jump. Each energy transition must be analyzed within the specific context of the system and its quantum properties.
