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Gamble123
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If some one could explain the concept it would be most apreciated.
What Is a Postulate in Quantum Mechanics?
- Thread starter Gamble123
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In summary, the concept of postulates is an important aspect of physical theories, particularly in the field of Nonrelativistic Quantum Mechanics. These postulates are assumed at the beginning of a theory and the rest of the theory's predictions are derived from them. There are different formulations of these postulates, such as Dirac's, von Neumann's, and Feynman's, each with their own mathematical expressions and representations. One postulate, the time evolution postulate, can be expressed in three different ways depending on the picture one adopts. These include the Schrödinger, Heisenberg, and interaction pictures. Additionally, there are different representations of the postulates, such as occupation number, position, and momentum.
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chroot
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It is something that is assumed at the "beginning" of a theory. The remainder of the theory's predictions are conclusions derived from its postulates. Postulates can be tested for correctness, but they are assumed, not derived.
Some examples of postulates:
The speed of light is constant for all observers.
Gravitational and inertial mass are the same.
- Warren
Some examples of postulates:
The speed of light is constant for all observers.
Gravitational and inertial mass are the same.
- Warren
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Each physical theory should be endowed with an axiomatical structure.From my reading and understanding experience,the best of them all is the one of (Nonrelativistic) Quantum Mechanics.Each if its 6 axioms has more fomulations (wording and mathematical expressions) depending upon the formulation of the theory:Dirac's (a.k.a.traditional),von Neumann's,Feynman's,...
There's one postulate (the IV-th,i.e.the time evolution postulate) which,in every formulation aforementioned,can be expressed in 3 different ways,depending upon the picture one adopts:Schrödinger,Heisenberg or interaction (a.k.a.Dirac-Tomonaga-Schwinger).And then of course you have the representations
ccupation number,occupation number-energy,position,momentum.Then of course you have the original formalism of matrix mechanics and wave mechanics,but this is not really a part of the axiomatical structure,as one finds them as particular realizations of the various ways of describing the concept of "physical state".
Daniel.
There's one postulate (the IV-th,i.e.the time evolution postulate) which,in every formulation aforementioned,can be expressed in 3 different ways,depending upon the picture one adopts:Schrödinger,Heisenberg or interaction (a.k.a.Dirac-Tomonaga-Schwinger).And then of course you have the representations
ccupation number,occupation number-energy,position,momentum.Then of course you have the original formalism of matrix mechanics and wave mechanics,but this is not really a part of the axiomatical structure,as one finds them as particular realizations of the various ways of describing the concept of "physical state".Daniel.
FAQ: What Is a Postulate in Quantum Mechanics?
What exactly is a postulate?
A postulate, also known as an axiom, is a statement or proposition that is accepted as true without proof. It serves as a starting point for reasoning and is used to derive other statements or theorems.
How is a postulate different from a theorem?
A postulate is a statement that is accepted as true without proof, while a theorem is a statement that is proven using other statements or postulates. In other words, a postulate is an assumption, whereas a theorem is a conclusion.
Can a postulate be proven?
No, a postulate cannot be proven because it is accepted as true without requiring proof. However, it can be used to prove other statements or theorems.
What is the purpose of postulates in mathematics?
Postulates serve as the foundation of mathematical reasoning. They provide a set of assumptions or starting points from which other statements and theorems can be derived. Without postulates, it would be difficult to prove any mathematical statement.
Are postulates universal or specific to a particular branch of mathematics?
Postulates are universal and can be applied to all branches of mathematics. However, different branches of mathematics may have their own set of postulates that are specific to their area of study. For example, Euclidean geometry has its own set of postulates that are different from those used in algebra.