Quantum Mechanics - Revision history

Milllo: /* States */

2020-05-27T06:07:40Z

States

Milllo: /* Math */

2020-05-05T17:03:36Z

Math

Milllo: /* Math */

2020-04-03T04:54:15Z

Math

Milllo: /* Math */

2020-04-01T19:40:35Z

Math

Milllo: /* Math */

2020-03-28T00:58:56Z

Math

Milllo: /* Math */

2020-03-24T19:52:05Z

Math

Milllo: /* Math */

2020-03-24T18:25:09Z

Math

Milllo: /* Math */

2020-03-24T16:49:55Z

Math

Milllo: /* Math */

2020-03-23T22:24:13Z

Math

Milllo: /* Math */

2020-03-23T22:14:26Z

Math

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 ==States==
-To get quantum mechanics one has to have a good understanding of the idea of states and there is no better way to understand something than to see it in action. So here is a two-state system that can be constructed easily. A video showing it in action will be posted soon:
+To get quantum mechanics one has to have a good understanding of the idea of states and there is no better way to understand something than to see it in action. So here is a two-state system that can be constructed easily. A video showing it in action will be posted at some point:
 Materials:
-* 4 bar magnets
+* 3 bar magnets with North/South on the sides rather than the ends
 * 1 swivel
-* 1 container to hold 2 of the magnets
+* 1 container to hold one of the magnets
 * Calipers
 Construction:
-# Divide three of the magnets into two groups by aligning two of them north-south, so now there is one magnet with north AND south on each end.
+# Fix one of the magnets to a hard surface with super-glue.
-# Place the pair into an oval container so the magnets are constrained but able to twist freely with the container.
+# Place another magnet into a container such as a centrifuge tube.
 # fix the third magnet to a surface.
 Two states in action:
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 For the calipers, the width will correspond to the photon size. A large width will be a high energy photon, while a small width is a low energy photon.
-The energy needed to change state is thus just enough to rotate the container barely past 90 degrees, the size of the caliper is barely big enough so that both sides of the caliper touch the container. Once past 90 degrees, the magnetic field of ths system will then push it (or pull it, depending on your point-of-view) to align the other direction.
+The energy needed to change state is thus just enough to rotate the container barely past 90 degrees, the size of the caliper is barely big enough so that both sides of the caliper touch the container. Once past 90 degrees, the magnetic field of this system will then push it (or pull it, depending on your point-of-view) to align the other direction.
 Discussion:
@@ Line 37: / Line 37: @@
 Two non-equivalent states:
-# Place the 4th bar magnet near the two-state system, below one end of the fixed magnet, but not close enough to cause them to repel each other.
+# Glue the third magnet near one end of the first fixed magnet.
 Discussion:

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 * [[Calculus]]
 * [[Statistics]]
-* Wave mechanics
+* [[Wave mechanics]]
 ==Topics in this Section==

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 * [[Trigonometry]]
 * [[Calculus]]
-* Statistics
+* [[Statistics]]
 * Wave mechanics
 ==Topics in this Section==

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 Most equations in math are derived, meaning that they can be derived from basic principles: given a thought problem and fundamental concepts, an equation solving the problem can be logically developed. One could either go through the derivation, which can be very long and convoluted, or accept that others have proven that a particular equation is true and instead focus on the uses and limitations of it. In other words, when an equation is presented and the author asks "This is true, do you believe me?". Answer yes.
-Examples are the sine equation, which involves tracking the position of a point on the circumference of a circle, and the wave equation, which involves tracking the position of a vibrating line fixed at both ends. There are many texts that provide these derivations and, for the moment, many will not be presented in this wiki. The resulting equations are very useful, especially in quantum mechanics, so a brief survey of the basic ones will be presented.
+Examples are the sine equation, which involves tracking the position of a point on the circumference of a circle, and the wave equation, which involves tracking the position of a vibrating line fixed at both ends. There are many texts that provide these derivations and, for the moment, will not be presented in this wiki. The resulting equations are very useful, especially in quantum mechanics, so a brief survey of the basic ones will be presented.
 A big problem in all science, but especially mathematics, is notation. Writing F(x) could mean "the value of the function F at x", or "x is a member of the group F", or even "the constant F multiplied by the variable x". Each meaning has dramatic implications for the use of math as a tool for a particular problem. This inconsistency is one reason why I dislike mathematicians. I will try to avoid this problem by listing notation meanings for each mathematical section, but be wary.

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 Now that we have a model of a two-state system along with a way to provide photons that will change the states, it would be nice to be able to describe the system logically and ultimately make predictions about it. This is where a tool like mathematics comes in. Unfortunately, regular math can't describe a system with states. The most complex regular math uses continua, like sine waves or curves, with differentials and integrals, infinitesimals and summations.
-Most equations in math are derived, meaning that they can be derived from basic principles: given a thought problem and fundamental concepts, an equation solving the problem can be logically developed. Examples are the sine equation, which involves tracking the position of a point on the circumference of a circle, and the wave equation, which involves tracking the position of a vibrating line fixed at both ends. There are many texts that provide these derivations and, for the moment, many will not be presented in this wiki. The resulting equations are very useful, especially in quantum mechanics, so a brief survey of the basic ones will be presented.
+Most equations in math are derived, meaning that they can be derived from basic principles: given a thought problem and fundamental concepts, an equation solving the problem can be logically developed. One could either go through the derivation, which can be very long and convoluted, or accept that others have proven that a particular equation is true and instead focus on the uses and limitations of it. In other words, when an equation is presented and the author asks "This is true, do you believe me?". Answer yes.
 A big problem in all science, but especially mathematics, is notation. Writing F(x) could mean "the value of the function F at x", or "x is a member of the group F", or even "the constant F multiplied by the variable x". Each meaning has dramatic implications for the use of math as a tool for a particular problem. This inconsistency is one reason why I dislike mathematicians. I will try to avoid this problem by listing notation meanings for each mathematical section, but be wary.

@@ Line 51: / Line 51: @@
 * [[Algebra]]
-* Trigonometry
+* [[Trigonometry]]
 * calculus
 * Statistics