Sunday, December 1, 2013

Hamiltonian01 An operator takes a function and returns another function. A Hamiltonian is a vector operator that manipulates a vector function, giving another function, and, as I recall, gives the energy levels.

I am sure that wikipedia has articles on these, and that they will answer your questions better than what you get here.
Even if I were willing to write an essay on this for you, to be honest, it has been 35 years since I took quantum mechanics, and my memory of it is hazy.

An operator is sort of like the next step beyond functions. A function takes a number and returns another number.
An operator takes a function and returns another function. For example, the gradient operator, [d/dx, d/dy, d/dz] returns the gradient of a function, that gradient being itself a function.
An operable is some function that is an allowable input to a given operator. Think in terms of the domain of a function; 1/[x-7] does not like x = 7

A Hamiltonian is a vector operator that manipulates a vector function, giving another function, and, as I recall, gives the energy levels.
An eigenfunction is one that when put through a given operator, returns a multiple of the original function.
The eigenvalue is the multiple.

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1 Summary of things you should already know

www2.ph.ed.ac.uk/~gja/qp/qp1.pdf‎
or measurement (Hamiltonian, or operator) and a measureable quantity (eigenvalue). There is no unique ... concepts for both vector spaces and function spaces. 1.6 Example of .... Consider manipulating the bras and kets. We can write a ...
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    The Hamiltonian and the Schrodinger Equation

    ocw.usu.edu/physics/classical-mechanics/pdf_lectures/12.pdf‎
    sides of this operator relation to an arbitrary state vector, representing the initial ... that one can manipulate the operators as if they were ordinary functions since.

  • Chemistry help quantum mechanics? - Yahoo Answers

    answers.yahoo.com › All Categories › Science & Mathematics › Chemistry‎
    Oct 29, 2010 - A Hamiltonian is a vector operator that manipulates a vector function, giving another function, and, as I recall, gives the energy levels.
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    Probability Current and Current Operators in Quantum Mechanics 1 ...

    www.phys.ksu.edu/personal/wysin/notes/qmcurrent.pdf‎
    Hamiltonian depends on a ”kinetic momentum” operator, π, defined by π = p − e c. ˆA. (2) .... The scaled vector potential α also is a real function of space and time. ...... If one can manipulate the operator and matrix for j(r) appropriately, one can ...

  • Dirac delta function - Wikipedia, the free encyclopedia

    en.wikipedia.org/wiki/Dirac_delta_function‎
    In applied mathematics, the delta function is often manipulated as a kind of ...... the normalized eigenvectors of a compact self-adjoint operator, any vector f .... The set of eigenvalues, in this case, is known as the spectrum of the Hamiltonian.
    You visited this page on 11/10/13.

  • Density matrix - Wikipedia, the free encyclopedia

    en.wikipedia.org/wiki/Density_matrix‎
    ... the experimenter does not know which particular states are being manipulated. ... In quantum mechanics, a quantum system is represented by a state vector .... For a finite dimensional function space, the most general density operator is of the form .... If the Hamiltonian is time-independent, this differential equation can be ...
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    Operations on States

    physics.mq.edu.au/~jcresser/Phys301/Chapters/Chapter11.pdf‎
    Given that an operator ˆA say, acting on a ket vector |ψ〉 maps it into another ket .... note that in general, the usual rules for manipulating exponential functions do ...... is expressed as an exponential function of another operator (the Hamiltonian).
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