\bra{\phi}The bra notation \bra{\phi} is part of the bra-ket notation used in quantum mechanics. It represents a row vector in a complex vector space, typically used to denote quantum states. The bra \bra{\phi} is the Hermitian conjugate (or complex conjugate transpose) of the ket \ket{\phi}, which is a column vector. This notation is essential in expressing inner products and quantum state transformations.
Represents the expectation value of the operator A in the state described by \ket{\psi}.
\bra{\phi} A \ket{\psi}Denotes the inner product of two quantum states, resulting in a complex number.
\bra{\phi} \ket{\psi}Represents the energy expectation value of the Hamiltonian H for the state \ket{\phi}.
\bra{\phi} H \ket{\phi}