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216 The Bible According to Einstein Chapter VI: The Wave Function Now the second way to understand quantum mechanics is through the quantum wave equation. And although it is not obvious, this approach shall be entirely equivalent to the path-integral approach. Chapter VII: Quantum Waves Now to understand the wave-function formulation one has to understand a wave. A wave is just an undulating motion such as the rise and fall of ocean water. |
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The New Testament 217
And since wave functions act as water waves, wave functions too can interfere. Thus quantum waves shall undergo constructive and destructive interference. An object shall more likely be at constructive-interference points. And an object shall less likely be near destructive-interference points. Chapter VIII: Wave-Particle Complementarity And the size of a wave unit shall be called its wave length – the distance between two crests. Now the length of a quantum wave shall have a special meaning – it shall determine when a wave function functions like a wave and is quantum mechanical and when a wave function functions like a particle and is classical. When the quantum wave length is long, the wave function shall be like a wave. And when the quantum wave length is short, the wave function shall be like a particle and not be like a wave. |
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218 The Bible According to Einstein
And since the momentum of an object is proportional to its mass, a heavy body shall always have a short quantum wave and thus behave as if it be a particle. Hence macroscopic bodies, such as blocks and balls and living bodies, never shall behave like waves. Only lightweight entities, such as atoms, nuclei, and subatomic particles, can have long waves. And when such lightweight entities have low momentum, they shall indeed have lengthy quantum waves and be wave-like. Thus, for example, shall the wave functions of low-energy electrons interfere. And when such electrons interfere, they shall create constructive and destructive interference regions – this shall be an electron interference pattern.^{196} And since the electrons in the atoms usually have low momentum, such electrons shall behave like waves. And the collection of waves of atomic electrons shall be called the electronic cloud. Now when an electron has high momentum, it shall have a short wave and be like a particle. And high-energy electrons, when they strike a target, shall produce localized, bullet-like destruction. (And a voice spake, saying Chapter IX: Discreteness Now often there shall be only discrete solutions to the quantum wave equation. And it is like unto the string of a guitar. And when the string is plucked, various vibrational motions are then possible. And if there be only one crest, then the crest appears in the middle of the string. And this is one solution. And if there be two crests, then a still point appears in the middle of the string and the crests appear on either side. And this is a second solution. And there can be vibrations with three crests. And in this case, one crest appears in the middle of the string and the other two emerge on either side of it. And between the middle crest and each side-crest is a still point. Thus there are two still points. And this is a third solution. And in general there can be solutions with any number of crests. And excluding the ends of the string, which are tied down and motionless, the number of still points on the string is one less than the number of the crests. Now for each type of vibration, there is a note. Thus there is a discrete set of sounds. And a guitarist with only these selected notes is unable to play tunes – to create other notes he uses his finger to shorten the string by pressing it against the neck of the guitar. But in the quantum world, there is no such way to shorten waves. (And a voice spake, saying
____________________ ^{196} The situation shall be like the pattern of light one sees at the bottom of a pool when the water is agitated. |
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The New Testament 219
Now a single vibrational motion of the guitar string shall in quantum mechanics correspond to what is called a state. A state shall by definition be a particular solution to the quantum wave equation. And a particle shall be in a particular state when it has a particular wave function. And the different notes of the guitar shall correspond to different energies. So each state shall have a unique energy – an energy level shall be the name for this. And since there are only distinct possibilities for states, there shall be only distinct possibilities for energies. And this is why the name quantum mechanics shall be used, for "quantized" means "discrete possibilities." Chapter X: Many-Body Quantum Mechanics Now when many objects and/or particles are present, there shall be a quantum wave equation for each particle or object. But only one wave function shall there be. And it shall solve all the wave equations simultaneously. And it shall be called the multiparticle wave function. And a multiparticle state shall be a particular solution of the quantum wave equations.
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^{197} Any state with an energy more than the ground state’s energy is called an excited state. Excited states can lose energy and "tumble" to the ground state. |
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220 The Bible According to Einstein
Now identical bosons shall behave the opposite of fermions. Not only shall they try to occupy the same position or same state, they shall do so maximally: The interchange of two selfsame bosons shall not change the state. And the situation shall be similar to that of identical red marbles: After putting all the marbles in a bag and shaking it, one shall no longer know which is which. Bosons are like unto red marbles; the multiparticle wave function for this system is like unto the bag. The indistinguishability of selfsame bosons shall make them behave in the most democratic way. And for example, if two neutral pions’ positions are interchanged, the world shall not be changed.^{199} Chapter XI: The Wave Equations And quantum mechanics shall rule all. It shall manifest itself for objects that are small. Quantum mechanics shall govern atoms, nuclei, and subatomic particles like photons, electrons, neutrinos, quarks and gluons. Now subatomic particles shall obey special quantum wave equations called relativistic wave equations. And larger microscopic objects shall satisfy the ordinary quantum wave equation, the so-called Schrödinger equation. Chapter XII: Quantum Angular Momentum And quantization shall apply not only to energy but to other quantum observables. And quantum observables shall be quantities that one can observe and measure, such as position, energy and momentum.
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^{199} Pions are elementary particles, which are bosons. See the Book of Subnuclear Physics. |
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The New Testament 221
And the amount of revolving of an object shall be its angular momentum. And since angular momentum is an observable, it shall be quantized. And the possible amounts of angular momentum shall be limitless but yet discrete. And these amounts shall be multiples of a fundamental unit, which is Planck’s constant. Thus there shall be states with angular momenta of zero, one, two, three, . . . multiples of this fundamental unit. Chapter XIII: Summary Quantum mechanics, |
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