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Review quantum basics Hermitian operators have realvalued observables

step inference rule input feed output step validity (as per SymPy)
1
  • 111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an initial equation.
  1. 9999999975
    \(\langle \psi| \hat{A} |\psi \rangle=\langle a \rangle\)
 no validation is available for declarations
2
  • 111696: conjugate transpose both sides
  • number of inputs: 1; feeds: 0; outputs: 1
  • Conjugate transpose of both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 9999999975
    \(\langle \psi| \hat{A} |\psi \rangle=\langle a \rangle\)
  1. 2394935835
    \(\left(\langle\psi| \hat{A} |\psi \rangle \right)^+=\left(\langle a \rangle\right)^+\)
 recognized infrule but not yet supported
3
  • 111890: distribute conjugate transpose to factors
  • number of inputs: 1; feeds: 0; outputs: 1
  • Distribute conjugate transpose to factors in Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 2394935835
    \(\left(\langle\psi| \hat{A} |\psi \rangle \right)^+=\left(\langle a \rangle\right)^+\)
  1. 1010393913
    \(\langle \psi| \hat{A}^+ |\psi \rangle=\langle a \rangle^*\)
 recognized infrule but not yet supported
4
  • 111104: declare assumption
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an assumption.
  1. 9294858532
    \(\hat{A}^+=\hat{A}\)
 no validation is available for declarations
5
  • 111634: substitute RHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 1010393913
    \(\langle \psi| \hat{A}^+ |\psi \rangle=\langle a \rangle^*\)
  1. 9294858532
    \(\hat{A}^+=\hat{A}\)
  1. 4948934890
    \(\langle \psi| \hat{A} |\psi \rangle=\langle a \rangle^*\)
 name 'Bra' is not defined
6
  • 111634: substitute RHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 9999999975
    \(\langle \psi| \hat{A} |\psi \rangle=\langle a \rangle\)
  1. 4948934890
    \(\langle \psi| \hat{A} |\psi \rangle=\langle a \rangle^*\)
  1. 2848934890
    \(\langle a \rangle^*=\langle a \rangle\)
 invalid syntax (<string>, line 0)
7
  • 111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 2848934890
    \(\langle a \rangle^*=\langle a \rangle\)
 no validation is available for declarations


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