Green Physics Magic!
April 16, 2024
Summary and Discovery
An upward arc, a simple curve can show
the basic equations' ideas from some branches of mathematics and the sciences:
For my discovery I read these amazing
textbooks and many, many more science books that are read more like novels!
Precalculus by James Stewart
Elements of Statistics by Mode
Calculus by James Stewart
College Physics by Randall Knight
College Physics for Scientists and Engineers by Randall Knight
Differential Equations by William Boyce
Linear Algebra by Gilbert Strang
Thermal Physics by Daniel Schroeder
Lectures on Physics Volumes 1-3 Richard Feynman
Nanostructures and Nanotechnology by Douglas Natelson
The following mathematical methods described in those textbooks can be
simplified into a The Little Mermaid Arc:
We find that for linear algebra, solving augmented linear matrices are for
systems of linear equations, and the operations are the 1) Delta, 2) Del
Operator, and 3) Addition Laws- [+ (is adding)- in other words is adding and
subtracting vectors or is solving systems of linear equations through the
Gauss-Jordan reduction method or the different methods, [x for vectors (is the
Del Operator, or multiplying)- is multiplying vectors through the cross product
to get 90-degree, perpendicular angles for solutions to linear algebra
equations, like for Maxwell's Equations (which are used to find the x-, y-, and
z-axis directions of the electric, magnetic, and propagating direction
components of electromagnetic waves- they go at the speed of light, by the
way)], [Also, a triangle, or the delta graphic, expresses other vector, or
angle quantities, than the cross product's standard 90-degree angle, and it is
used in time-dependent (which often involves movement) equations].
Also, the confusing terms from linear algebra are rank, dimension, basis, span,
linear independence and dependence, and homogeneous and nonhomogeneous
equations and from statistics are the boring three m's in mean, median, and
mode. The solutions to the linear equations from our first paragraph can be
described in form as y=mx+b, for which the general form is in an augmented
linear matrix is |33 |= |3,4,5 | |x,y,z|.
Also, in nanotechnology, the so-called Bloch Equations portray both the
periodic arrangement of atoms and the electron potentials (an electron
potential is the energy in electron volts (eV) of the electron in the valence
energy orbital, and the potential dies off or increases predictably in a linear
fashion with increasing space from the original, starting energy state of the
atom of the electrons in the crystals- like diamond, citrine, or calcite). One
can visualize a printed Bloch wave above a crystal whose atoms are formed like
this cool, repeating, periodic pattern of, say, citrine
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
The general and particular solutions of the Schrodinger Equation for finding a
"particle-in-a-box" is, similarly, mathematically shown in a wave 1) Aeix +
Be-ix; this for a complex vector space, where the y-axis maximum and
minimum values are 1 and -1, which represent the square of -i as 1 with the
square of i as -1; also, this equation is for electrostatic potential how it
drops off from an electron or set of electrons and then picks up with the
adjacent electron of the crystal lattice structure of each different element,
or crystal, as it is coming closer in the frame, or in the wave Ψ= Acoskx
+ Bsinkx, which represents the chances from 0 percent to one hundred percent-
the |Ψ|2 absolute values that show this percentage will
range 0 to 1 --0 to 100 percent-- for detecting a particle at a certain place
along the length, like, of a big glass aquarium tank with cool goldfish in it!
Also, the solutions for Ψ- this time for the energy values of the Matrix
Overlap Elements, involving multiple quantum wells (and, in extension, for the
addition or subtraction [ebb and flow] heights of all like ocean waves that
bump and grind into and out of each other- ha!) for time-dependent Hamiltonians
of the form CH12 and CH21. For all
waves, as you journey across the x-axis the changing, time-dependent radian
values are from 0 radians to 2π radians (a conventional way of writing the
radians is as four values 0, ½π, π, 3/2π, and 2π) and the heights along the
y-axis are 1 to -1 (this along the period, or total length, of the wave), and
they will show the different heights of the curves (waves) as you go along the
radian k-space values.
One gets the y-values of the functions cycling in the periods through inputting
the changing SOHCAHTOA Theta-angle values in the triangle for your Wavies,
I will name them.
Reference: SOH Sine: Opposite/Hypotenuse
CAH Cosine: Adjacent/Hypotenuse
Also, you find 90-degree angles for the perpendicular natures of Maxwell's
Equations for Electromagnetic Waves (for B [magnetic wave], E [electric wave],
and Z [direction of propagation at the Z-axis])- note all three are at a
90-degree angle, or are perpendicular to each other. The electric wave is
produced by a potential in a crystal or bulk material, which makes an electric
field that produces a force incident on a test charge (it can physically move a
charge, like the charge moved can be an electron). A magnetic wave is formed
from the Tri-Source (I made this term up!) of own-axis
spinning of the protons in the nucleus and the valence electron spinning around
its own axis as also it goes around this third value contributing to the total
magnetism, the angular acceleration: the electron's fast moving speed in a
circular path from the valence energy orbital and about the nucleus of the
atom.
Hamiltonians (H11, H22, H12,
H21 An upside-down triangle with a small upside-down
triangle graphed within it (I made this up also!)= There is a perpendicular
90-degree-angle value for a situation that is portrayed by H11 H22,
and the little triangle inside the Del 90-degree triangle is for when you have
with the different angles (i.e. with radians other than 0, π, π/2,
3π/2, and 2π) for conformations of things other than just with the 2 values. A
2-value conformation would be a cis-trans isomer, a chiral molecule, and a
two-state NH3 Ammonia molecule that has two shapes with
its atomic form that I read about in the discussion of Hamiltonians recently.
Also, the commutative-style regime extends in visualizibility and vulnerability
to Polarizing light (with elliptical polarizibility, circular, and regular
polarization [regular polarized light you have for Stern-Gerlach apparatuses,
and you find the final interference-filled light result in which all the light
was changing through each polarizing filter, or apparatus, from bra-ket notation
as the Psi final energy value with appropriate visual wavelength for the
lightbeams; Polarizing is following the Kronecker delta (the following lower
case δ is a Greek letter; no, not the delta, silly, which is also a Greek
letter D but upper case!) δ's |1||0|and the H22, H11,
H21, and H12 commutative laws, which extend
to Matrix Overlap Elements for multiple quantum wells and to waves (like
standing waves for the differing notes on violin and guitar strings).
Nonlinear cool stuff I like that is not described as like vacuous are fractals,
snowflakes (both of all kinds of shapes), ocean/river vortices (from chaos
theory), EPR (Einstein, Podolsky, Rosen) photon nonlocality and photon
entanglement of photons for quantum computing (one distant photon knows what
the other is doing, which is useful for non-binary <1 <2 quantum bits
[binary bits 0,1 are used for regular computers in a Boolean Logic sense of a
simple true/false or question and answer query]). Quantum computers are good
for cryptographic secret communications between parties in the fiber optic
networks, which provides great safety to both financial and personal data
nests.
Diagram for the movement of charge density in a changing magnetic field from
one location to another location (the density is made up of upward-arrow North
and downward-arrow South charges of an electron, manifested as spin-up and
spin-down particles in space, namely, by my appellation of Half-Valence
Diagram, where with the diagram you see the V, or population density shift
from being more of like the spin down than the spin up or vice versa.
Magnetism has to do with the three values of spin-orbit coupling [i.e. angular
acceleration and spin of an electron about its own axis] and the charge from
the nucleus where are the neutrons and the protons. Jon can form a colorful
crayon arc with curvilinear coordinates. The terms of spin-orbit coupling
should be written as integers for its values, I think, not as the confusing
1/2, 3/2, 5/2 for its values). The arc can be described by simple,
optimistic-curve, constant integers like 1, 2, 3, 4, and 5... This arc
can be like an isotherm, can be used in all of the mathematical equations in
physics, and can be imagined with all colors of your imagination!
I would like to thank my female
guiding light who has protected and watered me to grow as a plant does,
improving my social ability (I love going out to talk), intelligence, and
strength (my arm strength and my visual scanning perception in editing my books
are so valuable to me). I thank Daphne for my great gift. My female
elemental (like with the druids in fantasy myths) and nymph I love so much and
must always in my whole life love her for happiness given. I dedicate
this science abstract to the loving child Andrea!
Chapter 2
Discovery and Summary
All Matrix Overlap Elements involving (i.e. double quantum
waves), Wave Packets, and Waves. When
there is a moving wave thing heading forwards meeting another wave heading
towards it (like with the Double Quantum well with the interior of the well
where the interference is) and with the interference of any waves of wave
packets traveling. All answers will be
scalars for MOE’s and similar wave-similar elements, following the Ψ
polarization-state trends of the <012> +-34 bra-ket and kroenecker delta
δ=0 (for rest) δ=1 (for the kroenecker delta is for a definite state only for a
unique value, or constant; the other states will all have δ=0).
All Scalar (non-bold lettering k, for example) or Vector (a bold K). Answers from Sine and Cosine waves is, in
this instance, k-space of the form ekt, or, if you want eix,
e-ix, you will be able to employ a complex vector space, which is
regular space or k-space with all negative y-values as negative i’s, and, since
the square complex conjugate of an imaginary number is positive, all the
normalizable |Ψ|2 states will come out correct.
In short the female protectors curve is Stewart textbook, Randall
Knight College Physics. Here I first
learned of the properties or coolness of derivatives in velocities of, say,
cars and airplanes in College Physics. A
velocity quantity is the first derivate of the equation or function (f(x). The acceleration is the second
derivative. Also, I learned about
integrals in Calculus by Stewart and how you can orangeshade this is a new
verb- orangeshade or purpleshade or aquamarineshade or redshade to describe
various colors you can employ for shading the trapezoidal area under the graph
of the integral to give the value of the area and hence the scalar answer for
the integral, whether the form of the area is a definite or an indefinite (what
terms!- confusing) integral.
Also, I learned about integrals in Calculus by Stewart and how you
can orangeshade this is a new verb- orangeshade or purpleshade or aquamarineshade
or redshade to describe various colors you can employ for shading the
trapezoidal area under the graph of the integral to give the value of the area
of the trapezoid and hence the scalar answer for the integral, whether the form
of the area is a definite or indefinite (what terms!- confusing) integral. Fourier transforms can be used for infinite-space-
another idea like k-space but different.
Solutions of Differential Equations can be any general and all
elemental differential equations that, when added, will form the general equations
in form. A differential equation can
have as many powers of the y main variable as possible, like the y-value can
even be y’’’’’’’’’’, so you could have y’’’’’’ + 8y’’’’’ + 29y’’’’’ + 3y’’ = 33-
this is the main equation; you solve for y, and any combination of differential
equations will also add up to the first general equation you have to solve to
find all the graphing values in our case, or regime, of math. Y6 + 8y5 + 29y5
Sigma ii 3X+4, --à extending
the summation idea, you could remember trapezoidal areas of and under the
integral and take the Sigma as a paradigm even of limits as that can be extended to
be transforms that are almost exactly the true value of the integrated
area. Transforms are like the Fourier (0
[I made this up for a vertical z-axis line of any length for circular [also my
transform has three levels of freedom for diffraction of light through a
cardboard hole, where light looks the best]), the ½ Fourier series, and the 1
Fourier transform). Maxwell’s Equations
for a forces population density for lim-à infinity
of the curve-integral x-axis is the asymptote, asymptotal for x-, y-, z- axes values
as x approaches infinity for a curves.
For the Kids: Essay About Physics to Highly Simplify Mathematical Equations
A simple curve can represent the equations’ ideas from some branches of mathematics and science:
Algebra I
Algebra II
Pre-Calculus
Statistics
Calculus
Linear Algebra
Quantum Physics
Nanotechnology
Linear Algebra Can Be Represented by a Mom’s Curve:
Augmented Linear Matrices- For Systems of Linear Equations (From Linear Algebra)
Operations (Delta, Del, and Commutative Laws)
Also, Remove the Confusing Terms from Linear Algebra (Rank, Dimension, Basis)- (Continued…)
And the Banal Ones from Statistics (Mean, Median, and Mode)
Bloch Equations for The Periodic Arrangement of Atoms in Crystals From Nanotechnology (From Nanotechnology)
Schrodinger Differential Equation for a Particle-in-a-Box (From Quantum Physics)
Time-Dependent Hamiltonians (Introduced in Quantum Physics)
Nonlinear Waves (Wave Packets)
All Matrix Overlap Elements and for Double and Triple And More Quantum Wells and Similar Interferences for Waves
All Scalars and Vectors Answers from Sine and Cosine Waves of the form e to the kt, or e to the ix and e to the �"ix (For Complex Vector Space) From the Aforementioned Concepts
The Mom’s Curve is Like an Isotherm in the Calculus Textbook
Dear Reader, I had the curve drawn, but it did not appear- just visualize a simple curve for this drawing! And I dedicate this physics abstract to Andrea, my visitor from black and very deep outer space, thanking her most heartily!