Green Physics Magic

I love the topic of physics!

"Green Physics Magic!"

November 6, 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 I was enthralled in...

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) Ae^ix + 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 TOA: Opposite/Adjacent

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!

Chapter 2

Discovery and Summary

 

All solving of waves of Matrix Overlap Elements involving (i.e. double quantum waves) Wave Packets (nonlinear waves) and Waves occurs when there is a moving wave 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, which are wave elements, following the Ψ polarization-state trends for the Stern-Gerlach Apparatus of the <012> for the right numbers for the Stern-Gerlach Apparatus of the bra- ket notation and of the kroenecker delta δ=1 and d=0 notation (the kroenecker delta =1 for a definite state only for a unique value, or constant; the rest of the states will all have δ=0).

All wave discoveries are scalar (non-bold lettering k, for example) or vector (a bold K).  All answers obtained from Sine and Cosine waves can also be from the k-space cosine and sine waves that are of the form e^kt, or if you want e^ix  and e^-ix - you will be able to employ |Ψ|² states for the Schrodinger equation of finding a particle in a box.  You will be able to employ a complex vector space, which is regular space or k-space with all the negative y-values on the graphs 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 protector's curve is from the James Stewart Calculus and the Randall Knight College Physics textbooks.  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 derivative of the equation or function f(x) and 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, purpleshade, aquamarineshade, or redshade to describe various colors you can employ for shading with crayons 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 integral (a converging indefinite integral with a series can be used to express this! [what terms as definite and indefinite integral!- confusing]).

The solutions of differential equations can be any general and all the elemental differential equations that, when added, will form the general equations in form.  For the differential equations the particular solution can be written with different constants for the different ways of delineating the general solution employing commutative laws (e.g. division also!).  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 the particular solutions 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 to get, or generate, new starting y's also for your different equations to start the mathematics.

 

Σ_i 3X+4, --à extending the summation idea, you could remember trapezoidal areas of whose solutions are under the integral and take the Sigma as a paradigm even of limits as that can be extended to be infinite transforms that are almost exactly the true value of the integrated area.  

 

Chapter 3

Discovery and Summary

 

This exciting physics abstract discovery is for conceptualizing extra dimensions past the normally perceived three dimensions.  I was just cogitating how if there are two equal transforms, like a Fourier Transform that all head to an equal number on the x-, y-, and z- axes, then you can introduce and thus visualize well a space-time curved Einstein fourth dimension of time, and I visualized and imagined for this a delta operator in a Hermitian for an additional transform in the time dimension (that is not near the speed to light due to Lorentz invariance amongst axes).  There will be a 90-degree angle to portray the two transforms in complex vector space as not right on top of each other in the added dimensions.

Then draw with a crayon an upward line, but to better portray this is a curve tensors up with its own delta and the upside-down triangle Dal curl, as it were, for the Tri-Source values, and you can make yours into a colorful shapeship navigation compasses with straight and arced lines.  String theory would be extended to the advantage of curves for shapes and even curves joined with arrows that could mayve be more easily visualized with a circle multivariabled  of radii sets (i.e. circles with different radiuses could in K-space represent with these radiusus a vector with the varying value on the axes for the four x-, y-, z-, a- dimensions.  A vector of course representing a bundle of straight lines (i.e. all of them).  

All values are recognized under a general, commutative paradigm for the Tri-Source as limx>>> infinity, y>>>>infinity, and z>>>>infinity.  The Hermitian in complex vector space for perceiving the spaceship's compass gotten from the identical two transforms' arcs is the complex conjugate equation H_ijon, and the x- and y-axes of the complex conjugate are set at 90 degrees to each other.  The Tensor would be tensors in three dimensions and adding up to one grand tensor that represents the fourth dimension of time, and each of the visible electromagnetic light tensors would be considered as equal in order to get the final (0, 0, 0, 3) set of values with the three representing time and the 0's representing the uniform tensors (they are J_xy+ J_yz +J_xz and all four tensors are with the arc representing “a”- J_xyz(_a)!)  

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 with people), my intelligence, and my arm strength.  I thank Daphni for my great, amazing, miraculous (to me at least!) gifts.  I love Daphni, who is a female nymph and elemental (like with the druids in fantasy myths), who possesses the imperturbability and beauty of spring rain.  I love her so much and must always in my whole life love her for her unspeakably-groundbreaking happiness given.  I dedicate this physics abstract to the loving child Andrea, who is blithe, carefree, and most ingenuous, and let us not forget humble as well!  Andrea has a malicious edge of humorousness also!  She loves being the best!