“Mechanically” Defined Shapes
of Atomic Orbitals from Harvey E White book (1935)
“Introduction to Atomic Spectra“
He manufactured these images using a mechanical imaging device in 1935.
This page is effectively the same shape as teachers use today in high schools and university courses. Graduate level courses invoke quantum theory to explain these shapes do not exist in the real world.
Real-valued orbitals can be formed as linear combinations of mℓ and −mℓ orbitals, and are often labeled using associated harmonic polynomials (e.g., xy, x2 − y2) which describe their angular structure.
The Schrödinger equation is not the only way to study quantum mechanical systems and make predictions. Other formulations of quantum mechanics include matrix mechanics, introduced by Werner Heisenberg, and the path integral formulation, developed chiefly by Richard Feynman. When these approaches are compared, the use of the Schrödinger equation is sometimes called “wave mechanics”.
The equation given by Schrödinger is nonrelativistic because it contains a first derivative in time and a second derivative in space, and therefore space and time are not on equal footing. Paul Dirac incorporated special relativity and quantum mechanics into a single formulation that simplifies to the Schrödinger equation in the non-relativistic limit. This is the Dirac equation, which contains a single derivative in both space and time.
Another partial differential equation, the Klein–Gordon equation, led to a problem with probability density even though it was a relativistic wave equation. The probability density could be negative, which is physically unviable. This was fixed by Dirac by taking the so-called square root of the Klein–Gordon operator and in turn introducing Dirac matrices. In a modern context, the Klein–Gordon equation describes spin-less particles, while the Dirac equation describes spin-1/2 particles.
NEW Shape of “Electron”
Proposed by B. Vincent Crist
in 2003
(witness: Ramesh Joshi, PhD)
student of Hans Einstein at UCB
I claim that the electron itself exists in the shape of a
3-Dimensional
“Mobius” Structure
Mobius Shaped Electrons 