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| Raising a number to a non-integer power. |
| << < (3/13) > >> |
| SiliconWizard:
I guess already explained above. It's the exponentiation, and is explained there: https://en.wikipedia.org/wiki/Exponentiation An integer exponent is a particular case of exponentiation. |
| mark03:
What is this number i that you speak of? |
| T3sl4co1l:
--- Quote from: mark03 on May 27, 2020, 03:12:31 pm ---What is this number i that you speak of? --- End quote --- You must be 'j'oking ;D Tim |
| TimFox:
The best joke I encountered in a physics lecture was by the late Professor Ugo Fano at the University of Chicago (ca. 1976). He was demonstrating the quantum calculation of dielectric polarization, expressing the macroscopic result as the expectation value of the quantum calculation. He used quantum perturbation theory to relate the polarization to the applied E field, expressing the Hamiltonian (essentially the energy) as a function of E and the harmonic binding of electrons. He then performed a Fourier decomposition of E(t) into frequency components, an integral over w (I can't find lower-case omega here) of E(w) ei wt dw . One of the theory weenies in the first row objected, "Professor Fano, that Hamiltonian is not Hermitian!", by which he meant that the energy must be real and not complex. Prof. Fano erased the "i", replacing it by "j" and declared the Hamiltonian was now Hermitian. |
| TimFox:
I also learned that the formal definition of exponentiation in modern mathematics is the one involving logarithms, which is required when the exponent is not a rational fraction. It also allows raising a variable by a complex exponent. It reduces to the usual expression when the exponent is an integer or fraction. |
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