documentclass{article}
pagestyle{empty}
usepackage{amsmath}
begin{document}
 [
 boxed{c_i = sum_jA_{ij}}
 ]
 [
 boxed{c_i = langlepsi|phirangle}
 ]
end{document}

mybluebox[<top pad>][<bot pad>]{<contents>}

documentclass{article}

usepackage{color}
definecolor{myblue}{rgb}{.8, .8, 1}

usepackage{amsmath}
usepackage{empheq}

newlengthmytemplen
newsaveboxmytempbox

makeatletter
newcommandmybluebox{%
    @ifnextchar[%]
       {@mybluebox}%
       {@mybluebox[0pt]}}

def@mybluebox[#1]{%
    @ifnextchar[%]
       {@@mybluebox[#1]}%
       {@@mybluebox[#1][0pt]}}

def@@mybluebox[#1][#2]#3{
    sboxmytempbox{#3}%
    mytemplenhtmytempbox
    advancemytemplen #1relax
    htmytempboxmytemplen
    mytemplendpmytempbox
    advancemytemplen #2relax
    dpmytempboxmytemplen
    colorbox{myblue}{hspace{1em}usebox{mytempbox}hspace{1em}}}

makeatother

begin{document}
begin{empheq}[box={mybluebox[5pt]}]{equation*}
    c_i = sum_j A_{ij}
end{empheq}

begin{empheq}[box={mybluebox[2pt][2pt]}]{equation*}
    c_i = langlepsi|phirangle
end{empheq}
end{document}

documentclass{article}

usepackage{amsmath}
usepackage{empheq}
usepackage[most]{tcolorbox}

newtcbox{mymath}[1][]{%
    nobeforeafter, math upper, tcbox raise base,
    enhanced, colframe=blue!30!black,
    colback=blue!30, boxrule=1pt,
    #1}

begin{document}
begin{empheq}[box=tcbhighmath]{equation*}
    c_i = langlepsi|phirangle
end{empheq}

tcbset{highlight math style={boxsep=5mm,colback=blue!30!red!30!white}}

begin{empheq}[box=tcbhighmath]{equation*}
    c_i = langlepsi|phirangle
end{empheq}

begin{empheq}[box=mymath]{equation*}
    c_i = langlepsi|phirangle
end{empheq}

begin{empheq}[box={mymath[colback=red!30,drop lifted shadow, sharp corners]}]{equation*}
    c_i = langlepsi|phirangle
end{empheq}

end{document}

> newcommand{boxedeq}[2]{begin{empheq}[box={fboxsep=6ptfbox}]{align}label{#1}#2end{empheq}}
> newcommand{coloredeq}[2]{begin{empheq}[box=colorbox{lightgreen}]{align}label{#1}#2end{empheq}}

usepackage{framed}