Dependence of Constants of Electromagnetic Interactions Upon Electron Spatial Energy Characteristic - Progress in Organic and Physical Chemistry: Structures and Mechanisms - page 3

Using the known correlations = ɋ/ λ and

λ

= h/mc (where h = Plank constant,

ν

ν = wave frequency) from the Equation (5), we can obtain the equation of spectral

regularities in hydrogen atom, in which 2ʌ 2 ɟ 2 /hɫ = Ʉ.
Taking into account the main quantum characteristics of atom sublevels, and based
on the Equation (3) we have the following:

% s
%x s
%

P P

P

0

or P

0

,

Å Å

x s x

where the value ǻɊ 0 is equal to the difference between Ɋ 0 -parameter of i -orbital and
Ɋ cn -parameter of counting (parameter of the main state at the given set of quantum
numbers).
According to the rule of adding Ɋ-parameters of like-charged or homogeneous
systems for two orbitals in the given atom with different quantum characteristics and
in accordance with energy conservation law we have:

ɝɞɟ Ɋ E,Ȝ = spatial energy parameter of quantum transition.
Taking the interaction ǻȜ = ǻɯ as a magnitude we have:
"

% % %%
%%%%% %

P PP PP P
MMMMM M

' ' "

0 0 0

or

0 0 0

¬

% % - P P

' "

-

0 0

-

%% -

MM
M

P

®

Δ

Let us divide again by term :

0

2

% % M

¬

' "

% % - P P

dP

2

P -

0 0

-

0 0

x 0.

%% -

MM
M

2

where

® x dP

, that is:

dM

2

% M

2 0

2

% % M

Taking into account only those interactions when 2ʌǻ ɯ = ǻȜ (closed oscillator), we
get the equation similar to Schroedinger Equation for stationary state in coordinate ɯ :
2

dP P

2

0

4 Q

0

x 0

2 2

dx % M

h
mv

Since

% , then:

2 2 2

dP P dP 8 Q m

0

4 Q

2 0

mv

2 2

x 0 or

0

PE 0

0 k

dx

2

h

2

dx

2

h

2

2

mv
E = electron kinetic energy.

where

k

2