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Dirac notation
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Bras and kets compactly represent quantum states.
⟨ψ∣φ⟩States are kets |ψ⟩, duals are bras ⟨φ|, and inner products ⟨φ|ψ⟩ are amplitudes. Operators act as Â|ψ⟩. It makes abstract state space reasoning compact.
⟨x|ψ⟩ = ψ(x).
|ψ⟩ is not a function of x, but a vector.
In more detail
Dirac notation writes quantum states as kets, such as |ψ⟩, and their duals as bras, ⟨ψ|. Inner products ⟨φ|ψ⟩ give probability amplitudes.
Real-world uses
- Quantum computing papers use Dirac notation throughout.
- Physicists use it to write concise quantum expressions.
- Quantum researchers write states and inner products compactly using bra and ket notation.
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Frequently asked questions
What is a bra?
The dual of a ket, which gives the complex conjugate and transposed form.
What does an inner product give?
An amplitude for transitioning from one state to another.
What does the bracket mean?
It gives the overlap between two states, which is the amplitude for one state to be found in the other.
Related topics in Quantum Mechanics
Stark effect · Perturbation theory · Variational principle · Superposition · Measurement and collapse · Schrödinger's cat