Quantum Mechanics in Potential Representation and Applications

The following sections are included:

• Preface
• Introduction
• Contents

The following sections are included:

• The Structure of Atoms
• The Schrödinger Equation
• The Fundamental Forces
• References

The following sections are included:

• Introduction
• Diffusion of Quantum Waves
• The Quantum Diffusion of an Electron in the Hydrogen Atom
• Solution of the Quantum Diffusion Equation for the Tunnel Effect for a Rectangular Barrier
• Conclusions
• References

The following sections are included:

• The Interactions between Nucleons
• The Shell Model and Mean Field Potentials
• References

The wave function’s dependence on time and the coordinates of particles can be found when solving the following common Schrödinger equation:

The following sections are included:

• Introduction
• Nuclear Reactions and the Optical Model
• Inverse Tasks of Scattering
• References

The following sections are included:

• Introduction
• Solution in the Case of s-Waves
• The Case of Large Nuclei
• Numerical Results and Conclusions
• References

The following sections are included:

• Introduction
• General Solution
• Numerical Results and Conclusions
• References

The following sections are included:

• Introduction
• The Integral Equation for Positive Energies in the Potential Representation
• The Integral Equation for Negative Energies in the Potential Representation
• Numerical Results and Conclusions
• References

The following sections are included:

• Introduction
• Integral Equations for Positive Energies
• Connection of Potential Representation Method with Green’s Functions
• The Scattering Matrix
• References

The following sections are included:

• Introduction
• Obtaining Integral Equations
• Obtaining the Scattering Matrix
• References

The following sections are included:

• Introduction
• The Derivation of Integral Equations
• The Accuracy and Convergence of the Obtained Solutions
• Conclusions
• References

The following sections are included:

• Introduction
• Standard Green’s Functions
• References

The following sections are included:

• Green’s and Undefined Functions
• References

The following sections are included:

• Introduction
• Non-physical Solutions of the Radial Schrödinger Equation
• Derivation of the Integral Equation
• Results and Conclusions
• References

The following sections are included:

• Introduction
• Integral Equations for Negative Energies in the Potential Representation
• References

The following sections are included:

• Introduction
• Modelling the Solutions of the Schrödinger Equation with the Harmonic Oscillator Potential
• Green’s Functions for the Potential Representation
• The Accuracy of the Solutions Obtained
• Conclusions
• References

The following sections are included:

• Introduction
• Bounded Systems: The Two-Body Task
• The Many-Particles Task
• Solution for the Ground State of the Helium Atom
• Variation According to the Parameter Z
• References

The following sections are included:

• Introduction
• Transformation of the Hamiltonian for He Atom
• Conclusions
• References

We can consider the static properties and radioactive decay of nuclei when relativistic corrections for the masses of nucleons are included A[14, 15]. These corrections are increasing the binding energies of the neutrons and protons in the external shells and take part in the stability of superheavy nuclei A[16, 17] with the enlarging role of shell effects. In the experimental method for the production of neutron-rich (N = 184) superheavy nuclei by low-energy multi-nucleon transfer reactions using shell effects like in ${}_{54}{}^{136}\text{X}\text{e}$ collisions with ${}_{82}{}^{126}\text{P}\text{b}$ was proposed. Here, the stabilization effect of closed shells A[14] and the significant relativistic effects for masses A[14] of neutrons and protons by quantum diffusion A[21] in a large region by the excited states of projectiles and targets can be used. The relativistic corrections to the potential are positive and small and can compensate the negative corrections for the mass of light nuclei A[15]. The relativistic corrections for nucleon masses are very important for the definition of heavy and superheavy nuclei energy levels of external shells A[16]. The relativistic corrections of the mass depend on the principal and the orbital quantum numbers and do not have any influence on the definition of the constant of the spin–orbit interaction. The negative corrections for the mass or energy levels for protons and neutrons depend on nuclei and vary approximately from −0.2MeV to −1MeV. It is important for the interpretation of α- (alpha), β- (beta) and γ- (gamma) decays. The number of decays occurring during the time interval from t to (t + Δt)

The following sections are included:

• Introduction
• The Semi-relativistic Hamiltonian
• Results and Conclusions
• References

The following sections are included:

• Introduction
• Semi-relativistic Equation
• Methods and Results
• Conclusions
• References

The following sections are included:

• Introduction
• The Integral–Differential Semi-relativistic Equation
• Results and Conclusions
• References

The following sections are included:

• Introduction
• The Integral–Differential Semi-relativistic Equation
• Results and Conclusions
• References

The following sections are included:

• Introduction
• The Solutions of Integral–Differential Semi-relativistic Equation for the Singular Potentials
• The System of Integral Semi-relativistic Equations in the Hartree–Fock Approach
• Conclusions
• References

The following sections are included:

• Introduction
• The Solutions of the Integral–Differential Semi-relativistic Equation
• The Approximate System of Integral Semi-relativistic Equations
• Semi-relativistic Model for Charmonium and Bottomonium
• Conclusions
• References

The following sections are included:

• Bibliography of the Authors
• Index