fix latex in docstrings (#323)

Author: ytdHuang

src/correlations.jl

@@ -23,7 +23,7 @@ ExponentialSeries(; tol = 1e-14, calc_steadystate = false) = ExponentialSeries(t
         c_ops::Union{Nothing,AbstractVector,Tuple}=nothing;
         kwargs...)
 
-Returns the two-times correlation function of three operators ``\hat{A}``, ``\hat{B}`` and ``\hat{C}``: ``\expval{\hat{A}(t) \hat{B}(t + \tau) \hat{C}(t)}``
+Returns the two-times correlation function of three operators ``\hat{A}``, ``\hat{B}`` and ``\hat{C}``: ``\left\langle \hat{A}(t) \hat{B}(t + \tau) \hat{C}(t) \right\rangle``
 
 for a given initial state ``\ket{\psi_0}``.
 """
@@ -69,9 +69,9 @@ end
         kwargs...)
 
 Returns the two-times correlation function of two operators ``\hat{A}`` and ``\hat{B}`` 
-at different times: ``\expval{\hat{A}(t + \tau) \hat{B}(t)}``.
+at different times: ``\left\langle \hat{A}(t + \tau) \hat{B}(t) \right\rangle``.
 
-When `reverse=true`, the correlation function is calculated as ``\expval{\hat{A}(t) \hat{B}(t + \tau)}``.
+When `reverse=true`, the correlation function is calculated as ``\left\langle \hat{A}(t) \hat{B}(t + \tau) \right\rangle``.
 """
 function correlation_2op_2t(
     H::QuantumObject{<:AbstractArray{T1},HOpType},
@@ -111,9 +111,9 @@ end
         reverse::Bool=false,
         kwargs...)
 
-Returns the one-time correlation function of two operators ``\hat{A}`` and ``\hat{B}`` at different times ``\expval{\hat{A}(\tau) \hat{B}(0)}``.
+Returns the one-time correlation function of two operators ``\hat{A}`` and ``\hat{B}`` at different times ``\left\langle \hat{A}(\tau) \hat{B}(0) \right\rangle``.
 
-When `reverse=true`, the correlation function is calculated as ``\expval{\hat{A}(0) \hat{B}(\tau)}``.
+When `reverse=true`, the correlation function is calculated as ``\left\langle \hat{A}(0) \hat{B}(\tau) \right\rangle``.
 """
 function correlation_2op_1t(
     H::QuantumObject{<:AbstractArray{T1},HOpType},
@@ -149,7 +149,7 @@ end
 Returns the emission spectrum 
 
 ```math
-S(\omega) = \int_{-\infty}^\infty \expval{\hat{A}(\tau) \hat{B}(0)} e^{-i \omega \tau} d \tau
+S(\omega) = \int_{-\infty}^\infty \left\langle \hat{A}(\tau) \hat{B}(0)} e^{-i \omega \tau \right\rangle d \tau
 ```
 """
 function spectrum(

src/metrics.jl

@@ -8,7 +8,7 @@ export entropy_vn, entanglement, tracedist, fidelity
     entropy_vn(ρ::QuantumObject; base::Int=0, tol::Real=1e-15)
 
 Calculates the [Von Neumann entropy](https://en.wikipedia.org/wiki/Von_Neumann_entropy)
-``S = - \Tr \left[ \hat{\rho} \log \left( \hat{\rho} \right) \right]`` where ``\hat{\rho}``
+``S = - \textrm{Tr} \left[ \hat{\rho} \log \left( \hat{\rho} \right) \right]`` where ``\hat{\rho}``
 is the density matrix of the system.
 
 The `base` parameter specifies the base of the logarithm to use, and when using the default value 0,

src/qobj/functions.jl

@@ -10,7 +10,7 @@ export vec2mat, mat2vec
 @doc raw"""
     ket2dm(ψ::QuantumObject)
 
-Transform the ket state ``\ket{\psi}`` into a pure density matrix ``\hat{\rho} = \dyad{\psi}``.
+Transform the ket state ``\ket{\psi}`` into a pure density matrix ``\hat{\rho} = |\psi\rangle\langle\psi|``.
 """
 ket2dm(ψ::QuantumObject{<:AbstractArray{T},KetQuantumObject}) where {T} = ψ * ψ'
 

src/qobj/operators.jl

@@ -408,7 +408,7 @@ sigmay() = rmul!(jmat(0.5, Val(:y)), 2)
 @doc raw"""
     sigmaz()
 
-Pauli operator ``\hat{\sigma}_z = \comm{\hat{\sigma}_+}{\hat{\sigma}_-}``.
+Pauli operator ``\hat{\sigma}_z = \left[ \hat{\sigma}_+ , \hat{\sigma}_- \right]``.
 
 See also [`jmat`](@ref).
 """
@@ -487,7 +487,7 @@ end
 @doc raw"""
     projection(N::Int, i::Int, j::Int)
 
-Generates the projection operator ``\hat{O} = \dyad{i}{j}`` with Hilbert space dimension `N`.
+Generates the projection operator ``\hat{O} = |i \rangle\langle j|`` with Hilbert space dimension `N`.
 """
 projection(N::Int, i::Int, j::Int) = QuantumObject(sparse([i + 1], [j + 1], [1.0 + 0.0im], N, N), type = Operator)