Exactly. Also known as Difference Calculus. It has some very interesting properties as explained here.. http://www.math-math.com/2018/02/the-calculus-that-got-ignored.html … and a famous "quantum application" here.. http://www.math-math.com/2016/05/simple-harmonic-oscillator-using.html …
Calculus students know that lim [f(xo+h) - f(xo)]/h as h -> 0 is the derivative of f) at xo. However, if we let x = qxo, where q is a fixed number not 1, and h a fixed number and do NOT TAKE THE LIMIT, we enter the fascinating world of quantum calculus ->https://bit.ly/3855z7R
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The difference, of course, is that when we think of difference calc we think of approximation and numerical analysis, but when we write the finite difference as [f(qx) - f(x)]/[(q-1)x] its possible to do a q-analysis, complete with equations for higher derivatives, etc.
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I have seen something similar in relation to q-deformed Lie algebras, in particular su(2). But in that case, q is a root of unity (and, IIRC, in relation to quantum gravity, ends up being related to the cosmological constant). Is quantum calculus a generalisation of this?
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I can't give you any accurate advice on that, but if you find Victor Kac's book Quantum Calculus online, it is written from a math and physics perspective.
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Sir! I m doing my doctoral research in Geometric Function Theory in context of q-calculus.
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T. Ernest book "A Comprehensive treatment of q-calculus" is also wroth reading.
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This is a wonderful website!
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Yeah, why not abuse the word quantum even more.
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Are there connections with Robinson's Nonstandard Analysis?
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Oooh! That sounds interesting
Any nice Gedankenexperiment or application on this, without going through the Math first?Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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