We prove the existence of a Hamiltonian with ionization energy as part of the eigenvalue, which can be used to study strongly correlated matter. This eigenvalue consists of total energy at zero temperature ($E_{0}$) and the ionization energy (𝜉). We show that the existence of this total energy eigenvalue, $E_{0} \pm \xi$, does not violate the Coulombian atomic system. Since there is no equivalent known Hamilton operator that corresponds quantitatively to 𝜉, we employ the screened Coulomb potential operator (Yukawa-type), which is a function of this ionization energy to analytically calculate the screening parameter (𝜎) of a neutral helium atom in the ground state. In addition, we also show that the energy level splitting due to spin-orbit coupling is inversely proportional to 𝜉 eigenvalue, which is also important in the field of spintronics.

Einstein, Podolski and Rosen (EPR) have shown that any wavefunction (subject to the Schrödinger equation) can describe the physical reality completely, and any two observables associated with two non-commuting operators can have simultaneous reality. In contrast, quantum theory claims that the wavefunction can capture the physical reality completely, and the physical quantities associated with two non-commuting operators cannot have simultaneous reality. The above contradiction is known as the EPR paradox. Here, we unambiguously expose that there is a hidden assumption made by EPR, which gives rise to this famous paradox. Putting the assumption right this time leads us not to the paradox, but only reinforces the correctness of the quantum theory. However, it is shown here that the entanglement phenomenon between two physically separated particles (they were entangled prior to separation) can only be proven to exist with a `proper’ measurement.

We derive the trial Hall resistance formula for the quantum Hall metals to address both the integer and fractional quantum Hall effects. Within the degenerate (and crossed) Landau levels, and in the presence of changing magnetic field strength, one can invoke two physical processes responsible for the electron conduction and quantum Hall effects in Fermi metals. One of the process requires the Pancharatnam wavefunction transformation, while the second involves electron transfer between two orthogonalized wavefunctions (within the degenerate and crossed Landau levels). We discuss the relevant physical postulates with respect to these physical processes to qualitatively reproduce the measured Hall resistance’s zigzag curve for both the integer and the fractional filling factors. Along the way, we give out some evidence to contradict the postulates with experiments.

We make use of the ionisation energy theory, Ramachandran interaction theory and the energy-level spacing renormalisation group technique to extend the Drude Hamiltonian to derive the Ramachandran pairing mechanism. This particular mechanism is exploited to explain the notorious discontinuous jumps in the specific heat data at critical points in both He-4 and He-3 superfluids. The well-known spin states (due to Balian–Werthamer and Anderson–Brinkman–Morel theories) and the Leggett’s spontaneously broken spin-orbit symmetry are shown to enhance Ramachandran attraction between two He-3 atoms without the need to invoke the spin-induced pairing or the phonon-mediated Cooper pairing mechanism in superconductors. In addition, we shall show physically that the spin-exchange mechanism can neither cause pairing between electrons nor between He-3 atoms.