Improving Teaching Particle-in-a-Box by Relationship to the Bose "Cylinder Surface" so 1D axis and 1D is the Subshells Ring-spring Set

Students struggle in Molecular Physical Chemistry for Engineers with the Concept of 'Particle-in-a-Box'. It is too abstract with its 2D math in a 3D universe. That failure rate of comprehension is one of the highest weak areas in physics education.

However, by making 1D as radius dimension and the 2nd 1D into the Subshells Ring-spring Set as the towards-the-axis direction of the longitudinal subshell set as a circle, the path from a physical atomic model to 2D math becomes teachable. That is 1D radius with a overall axis zenith (z) direction, and 1D towards-the-axis become the 1D circle of chemistry defined by that atomic model with a premagnetic axis.

First, this model relates to the Periodic Table logic of 1D as 2 poles x the square in the other 2D (circle), then interlaced to get teh Rows fo the Periodic Table.

Further, this method moves directly by Relationship to the Bose "Cylinder Surface" so 1D is the Subshells Ring-spring Set. Bose's proof of quantum mechanics, recognized and used by Einstein for his proof of the Ideal Gas Law is one of the important foundation of subatomic physics.

Further, the (PI*radiusSquared) gets mapped to the Born Rule needed for probabilty theory taught later in the course.

The implication is that the '2D box' becomes teachable by the integration with these other concepts.

In this short talk, a 'Particle-in-a-Cylindrical-Ring-Spring' gets mapped to the current textbook methods of Particle-in-a-Box.