another origin of square energy

[AntonioLao]

One simple derivation of energy level in quantum mechanics is given by E = nh/8mL. This equality expression indicates that the square of the principal quantum number n multiplied by the square of Planck’s constant of action h divided by the product of the numerical constant 8, mass m, and the square of length L gives the value of the energy level E. By simply transposing m to the left-hand side thus becoming a multiplicative factor instead of a right-handed divisor then multiplying both sides by the square of light speed c, the left-hand side clearly becomes the square of energy since E = mc, that is, E = c nh/8L. Furthermore, grouping all physical constants and algebraic variables together E = (n/L)(c h)/8. For this to be completely meaningful, the first E must be of the same magnitude as the second Ē derived from mc. Otherwise, only the equality of the dimensionality of square of energy is implied such that EĒ = (n/L)(c h)/8 and E is not necessarily always equal to Ē in their corresponding magnitudes.


The natural tendency that E is not always equal to Ē is the key concept that made quantum mechanics possible and is the underlying cause of Heisenberg’s uncertainty principle as well as Einstein’s principle of uncertainty for time parameter and energy. This inequality is extended deeper into the fine structure of atomic spectral analysis deriving additional sets of quantum numbers (for example, the magnetic quantum number and the spin quantum number in addition to the principal quantum number and orbital quantum number for the precise descriptions of bound electrons in atoms). In the classical sense, the equality of E and Ē becomes the principle of energy degeneracy. In the subnuclear domain of elementary particles of quarks and leptons, the inequality of E and Ē theoretically implies the existence of distinct topologies which are equal in magnitude and equality of geometric shape and size but not equal in their directionality. Quantizing these different directional invariance properties becomes a quantum theory of direction or equivalently speaking a quantum theory of space-time. This principle of directional invariance is clearly hinted by the fundamental theorem of quantum mechanics such that the left product of two conjugate variables is never equal to their right product that is AB ≠ BA or AB – BA > 0 assuming that AB is always greater than BA. This can never be true if A and B are real numbers. Fortunately, it can be true if and only if A and B are special forms of square matrices. These special matrices are rigorously discussed in any textbook of quantum mechanics. Nevertheless, for a quantum theory of space-time, unique special forms of square matrix conveniently called Hadamard matrices must be used such that AB = aB, AA = bA, and BB = gA where a, b, and g are all positive integers. These show the product symmetries of 1/3 and 2/3 important to the color and electric charge configurations of quarks.

[mkirkpatrick]

Well I am left handed and have been called a square,so I can identify with this!


regards michael.

[AntonioLao]

Fom completeness you also need a right-handed square. If you don't agree try asking someone who has to go through life with only one arm or one leg. It is not the same for them to be productive although I saw one with no arms who can paint with his toe.

[mkirkpatrick]

Fom completeness you also need a right-handed square. If you don't agree try asking someone who has to go through life with only one arm or one leg. It is not the same for them to be productive although I saw one with no arms who can paint with his toe.

Yes I saw that,it was a film I believe.

regards michael.

[AntonioLao]

I understand human brains can be separated into the left and the right. My question is if both left and right brain are damaged would we still have any consciousness of physical reality?