POSSIBLE TYPES OF STATISTICAL INFORMATION ABOUT A SYSTEM 3 The Schrödinger equation was devised to find the probability of finding the particle in the narrow region between x and x+dx, which is denoted by P(x) dx. The function P(x) is the probability distribution function or probability density, which is found from the wave function ψ(x) […]
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POSSIBLE TYPES OF STATISTICAL INFORMATION ABOUT A SYSTEM 2 In modern science there is a tendency of generalization or extension of one principle to others. For example; the Schrödinger equation in the so-called one dimension (actually it contains a second order term; hence cannot be an equation in one dimension) is generalized (?) to three
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POSSIBLE TYPES OF STATISTICAL INFORMATION ABOUT A SYSTEM 1 Our statistical information about a system may always be expressed by giving the expectation values of all observables. Now the expectation value of an arbitrary observable F, for a state whose wave function is φ, isIf we do not know the state of the system, but
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The essence of creation is accumulation and reduction of the number of particles in each system in various combinations. Thus, Nature has to be mathematical. But then physics should obey the laws of mathematics, just as mathematics should comply with the laws of physics. We have shown elsewhere that all of mathematics cannot be physics.
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The fundamental “stuff” of the Universe is the same and the differences arise only due to the manner of their accumulation and reduction – magnitude and sequential arrangement. Since number is a property of all particles, physical phenomena have some associated mathematical basis. However, the perceptible structures and processes of the physical world are not
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