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I'm reading from "Quantum Physics for Dummies", by Steven Holzner. In chapter two, entitled "Entering the Matrix: Welcome to State Vectors", the author introduces the notation for a gradient of a wave function.

Gradient operator

I understand all of the complement, but what confuses me is the use of the relationship operators, what do they signify in this context? How can you compare a partial derivative with a basis vector?

Qmechanic
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mcchucklezz
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    Having seen only these few lines I would definitely recommend to get the basics from some other book. Gradients of state vectors are a gross abuse of notation. – noah Sep 15 '17 at 16:03
  • @noah would you have any recommendations? – mcchucklezz Sep 15 '17 at 16:04
  • Not off the top of my head, no. But I'm sure you can find some at https://physics.stackexchange.com/questions/33215/what-is-a-good-introductory-book-on-quantum-mechanics. I just felt the need to mention that this is not a quality source. – noah Sep 15 '17 at 16:07
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    Throw the book away. – DanielC Sep 15 '17 at 16:23

2 Answers2

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This is typeset terribly. What it is supposed to mean is ket-vectors in Dirac notation, which are usually set with an "rangle" ($\rangle$) and "langle" ($\langle$), not > and <.

noah
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Unfortunately the author misuses the bra-ket notation. A state should be written in the form

$$ | \phi \rangle $$

instead of $|\phi >$. This way, the gradient should appear as

$$ \nabla |\psi\rangle = \frac{\partial}{\partial x}|\psi\rangle {\bf i} + \frac{\partial}{\partial y}|\psi\rangle {\bf j} + \frac{\partial}{\partial z}|\psi\rangle {\bf k} $$

caverac
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