How are wavefunctions and eigenkets used differently in quantum mechanics?

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Discussion Overview

The discussion revolves around the different treatments of wavefunctions and eigenkets in quantum mechanics, particularly contrasting the approaches of various authors such as Griffiths and Sakurai. Participants explore the implications of these different representations in both theoretical and practical contexts, addressing the confusion that arises from these varying methodologies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that Griffiths focuses on wavefunctions while Sakurai emphasizes eigenkets, leading to confusion regarding their applications.
  • One participant explains that wavefunctions can be viewed as coefficients in a state's expansion on the position basis, questioning how operators act on them.
  • Another participant elaborates on the mathematical formalism, stating that a pure state is represented by a ray in Hilbert space, and observables are represented by self-adjoint operators.
  • It is mentioned that the action of an operator on a wavefunction results in another function, providing an example with the momentum operator.
  • Some argue that while wavefunctions are practical for non-relativistic quantum mechanics, the abstract formalism may simplify problem setup and conceptual understanding.
  • A participant suggests that a deeper mathematical understanding is necessary to grasp the subtleties of these approaches, recommending advanced texts like Ballentine.
  • There is acknowledgment that both approaches have merits, but they can be confusing when used simultaneously.

Areas of Agreement / Disagreement

Participants generally agree that both wavefunction and eigenket approaches have their advantages and disadvantages, particularly in different contexts of quantum mechanics. However, there is no consensus on which approach is superior or more intuitive, indicating an ongoing debate.

Contextual Notes

Some participants highlight that the discussion is limited to non-relativistic quantum theory, noting that the treatment of wavefunctions may differ in relativistic contexts.

  • #31
micromass said:
Don't excuse yourself for asking. We are here to answer questions like yours!

But yes, ##\psi(x)## is a scalar, so you can treat it like one.

The wavefunction ##\psi## itself must be treated as a vector.

Thank you for your help!
 

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