The Bohr equation

Matthew E. Cross, Emma V. E. Plunkett

Edward T. Gilbert-Kawai, Marc D. Wittenberg

Espen Gaarder Haug

The Bohr radius was derived using the non-relativistic de Broglie approximation, not the relativistic de Broglie equation. In this work, we will derive a relativistic Bohr radius from both the relativistic de Broglie approximation and relativistic kinetic energy. The Bohr model of the hydrogen atom has since been replaced by modern quantum mechanics and the Schrodinger equation. It is well known that the Schrodinger equation confirms the first Bohr radius as the most probable radius, but the Schrodinger equation itself is non-relativistic. The Dirac equation can likely be used, but there seem to be very few publications on the relativistically corrected Bohr radius. This is something we will discuss.

Tao Liu

By calculating the Bohr-radius of hydrogen atom with the assumption of Bohr theory,uncertain relation,Schrdinger's equation and wave function,the semi-classic and the semi-quantum in the assumption of Bohr theory can be comprehended deeply.The uncertain relation is proved as the result of the undulatory theory for micro-particles.The electron in hydrogen atom obeys the Schrodinger's equation.The solution of the equation is a wave function,namely a probability wave.

Xiao En Wang

According to the energy relationship of the ground state solution of a hydrogen atom using the Schrödinger equation, the kinetic energy of an electron at twice the Bohr radius becomes zero. The electron has zero kinetic energy, which means it is dead, indicating that the energy relationship used in the Schrödinger equation is incorrect. Then, the reasons for both the chaotic energy relationship of the Schrödinger equation and the half frequency problem encountered by Bohr are analyzed. Bohr only considered Coulomb force and established an equation with centrifugal force, but he did not consider Lorentz force. So, the frequency he obtained must be multiplied by 1/2 to match the experimental value. This article also analyzes other issues related to the Schrödinger equation.