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I Quantum Superposition, Linear Combinations and Basis

  1. Jan 18, 2017 #1
    Hello, just a quick question.

    I am aware that a a state in a space can be written as a linear combination of the basis kets of that space

    ψ = ∑ai[ψi]

    where ai are coefficients and [ψi] are the basis vectors.

    I was just wondering is this a linear superposition of states or just a linear combination?

    Can it only be a linear superposition if the basis kets are eigenstates of some operator?

    Thank you
     
  2. jcsd
  3. Jan 18, 2017 #2

    blue_leaf77

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    I don't know if it's necessary to consider them different. The traditional way is that, say you have two vectors ##v_1## and ##v_2##. The linear combination between them is a vector such that ##v = a_1v_1 + a_2v_2## for some scalar ##a_1## and ##a_2##. Very strictly speaking, in that equation ##v_1## and ##v_2## do not superpose, instead ##a_1v_1## and ##a_2v_2## do. Do you get the idea now?
     
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