Figure 2.5.1: Heisenberg "Uncertainty Principle" Experiment

A comparison of Maple and Mathematica . (Mathematica to be used for solving the Schrodinger Equation for the "Particle-in-a-1D-Box"):

Maple input: >deqPB: =diff (y(x),x,x)=-E* y(x);

Maple output:

dsolve (deqPB,y(x));
deqPB:=

y(x) = -Ey(x)
y(x)=_C1

+_C2

Mathematica input: DSolve [y"[x]+E *y[x]==0,y[x],x]

Mathematica output:

{{y[x] ->

C[1] +

C[2}}

Mathematica files:

Solving the Schrodinger Equation for the "Particle-in-a-Box"
"Particle-in-a-Box" Wave-Functions 1-D and 2-D

Rewriting the Schrodinger equation in spherical coordinates:

The EXACT solution!!:

where

this implies: n, l, m, the quantum numbers, completely specify

.
Orbital Size:

Orbital Shape:

Orbital Direction:

note:

n only!

Meaning of

via

is a complex number, i.e.,

= a + bi

is a real number, i.e., = = (a+bi)(a-bi)

: "probability density distribution" for the electron, i.e., probability / vs. electron position (vector)
: "radial probability density distribution" for the electron, i.e., probability/dr vs. electron radial position .