In the first case, it’s a so-called ordinary differential equation. The function can be real-valued or complex-valued, and it can be a function involving only one variable (such as y = y(x), for example) or more (such as u = u(x, t) for example). Indeed, from a mathematical point of view, a differential equation (such as a wave equation) relates a function (such as a wave function) with its derivatives, and its solution is that function or – more generally – the set (or family) of functions that satisfies this equation. Indeed, I may have been sloppy here and there – I hope not – and so that’s why it’s probably good to clarify that the wave function (usually represented as Ψ – the psi function) and the wave equation(Schrödinger’s equation, for example – but there are other types of wave equations as well) are two related but different concepts: wave equations are differential equations, and wave functions are their solutions. The title above refers to a previous post: An Easy Piece: Introducing the wave function. It is, therefore, still quite readable-even if my views on these matters have evolved quite a bit as part of my realist interpretation of QM. Pre-scriptum (dated 26 June 2020): This post did not suffer from the DMCA take-down of some material.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |