Maximum Entropy Principle Table of Contents TOC
- Maximum Entropy Principle Table of Contents TOC
- Private: Derivation of the Planck Relation and Maximum Entropy Principle
- Maximum Entropy Distribution for Random Variable of Extent [0,Infinity] and a Mean Value Mu
- The Maximum Entropy Principle – The distribution with the maximum entropy is the distribution nature chooses
- Use of Maximum Entropy to explain the form of Energy States of an Electron in a Potential Well
- Langrange Multiplier Maximization Minimization Technique
- Derivation of Nyquist 4KTBR Relation using Boltzmann 1/2KT Equipartition Theorem
- Heuristic method of understanding the shapes of hydrogen atom electron orbitals
- Derivation of the Normal Gaussian distribution from physical principles – Maximum Entropy
End TOC
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Have you ever wondered why the dumbell shape of the N=2 quantum state of the hydrogen atom. I have! The Schrodinger wave equation gives you the results. But WHAT are you looking at? I have finally solved the problem of understanding the shape of the solutions. I did it while riding a bicycle in front of the electric driveway door waiting for it to open. It opens like a standard garage door on a house. I hate to just sit their with my leg on the ground so I started by riding the bicycle in a circle as the door rises. When the door is fully open I ride in and park. You can see my orbit in the picture below: One day the owner of the complex of houses was parked right in front of the door with the car extending into the street where I normally ride in a circle. I was thus constrained as show in the following diagram. The figure 8 felt most efficient given the contraint of not being able to go in a circle and wanting to loiter on spot until the path was clear. Maximum entropy principle wants to make my path as gentle as possible given the constaint of the circle not being allow.
Riding my bicycle in a figure 8 pattern Thus it is with the N=2 orbital. The N=2 orbital in an unexcited atom is only filled when there is an electron already filling the circular N=1 orbit. This filled orbit is the constraint of the car in the bicycle example. Its taken a long time to know the WHY of this. I solved the schrodinger for the hydrogen atom a long time ago. But I did not understand the why. Now I am sure that this same method applies the the higher N Numbers. The N number is the number of wave lengths in a full orbital path. Since the dumbell shape requires 2 wavelengths minimum. I feel better now! The Schrodinger wave equation yields minimum time / maximum entropy solutions. From this I deduce that an electron when in a state in an atom it is in Free-fall. Free fall is the condition of minimum time. However in free-fall there is no force on the particle. Also noting that accelerated charges radiate leads me to the conclusion that indeed the electron is spread out into the entire space of the orbital and not just a billiard ball whipping around in an orbit. This is very much a standing still wave. Why doesn't the electron just fall down onto the proton of the hydrogen atom? I think that might be due to the electron not liking to be stuffed into too small of a box. The electron most likely can sit on the proton with some probability but since it would undergo massive "compression" to do so it has an extremely high probability of leaking out of this state and into the N=1 state to get jiggy with it.
Quantum Mechanics Table of Contents TOC
- Quantum Mechanics Table of Contents TOC
- ASU Quantum Mechanics for Engineers 434 Notes from Year 2001
- Book: Advanced Quantum Mechanics – Freeman Dyson
- Book: Notes on Quantum Mechanics
- Quantum Mechanics Entanglement and Quantum Computation Summary List
- Quantum Mechanics and Entanglement Experiment with Single Photon Detector
- Summary Outline of Richard Feynmans Thesis – Framework for learning QED and Quantum Mechanics in general
- Quantum Computing Video strips down computing mechanics explanation to minimum
- Quantum Mechanics Computing for Computer Scientists
- Quantum Mechanics Money from Knots
- Quantum Mechanics Logic
- Video: Erann Gats explanation of quantum entanglement, measurement and interpretations
- Leonard Susskind Quantum Entanglement Lecture 2006
- Quantum Mechanics Entanglement and Spooky Action at a distance
- Quantum Computing Parallelism Explained
- On the Theory of Quanta Louis-Victor de Broglie 1892-1987
- Entangled-Light-Emitting Diode
- PAM Dirac Lectures in New Zealand 1975
- Leonard Susskind Lecture Series Play Lists
- Video: Spooky Actions At A Distance?: Oppenheimer Lecture – David Mermin – and Rhetorical Homework Problem Solution
- Lectures on Quantum Computation by David Deutsch – Includes Best Grover Search Algorithm Explanation Unit 6
- Basic Polarized Photon Entanglement Experiment
- Private: Quantum Computing Book Collection
- Video: KITP Lecture : Putting Weirdness to Work: Quantum Information Science
- Private: Derivation of the Planck Relation and Maximum Entropy Principle
- Derivation of Nyquist 4KTBR Relation using Boltzmann 1/2KT Equipartition Theorem
- Heuristic method of understanding the shapes of hydrogen atom electron orbitals
End TOC
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