List of eigenvalues of a list of abstract states

Question

Suppose I have the states \Psi, \Phi and \Zeta and I also have the following relations given by the operators A and B when acting in the states

A.\Psi=1*\Psi;
B.\Psi=2*\Psi;
A.\Phi=3*\Phi;
B.\Phi=4*\Phi;
A.\Zeta=3*\Zeta;
B.\Zeta=4*\Zeta;

where I am denoting by a dot the action of A and B. If I define

list1={A,B};
list2={10*\Psi,5\Phi + \Zeta};

And, from them, I multiply the two lists

list3=Table[Table[i.j,{i,list1}],{j,list2}]
    

giving

list3={{A.10*\Psi,B.10*\Psi},{A.(5\Phi + \Zeta),B.(5\Phi + \Zeta)}}
     ={{1*(10*\Psi),2*(10*\Psi)},{3*(5\Phi + \Zeta),4*(5\Phi + \Zeta)}}

where the second line comes after using the relations given in the first lines of code.

How do I make Mathematica write only the eigenvalues of the operators A and B when acting on list2 (I want it to write {{1,2},{3,4}} from list3)?

Answer 1

As @Domen wrote in the comments, the question can be answered by the following code

A[\[Psi]] = 1;
B[\[Psi]] = 2;
A[\[Phi]] = 3;
B[\[Phi]] = 4;
A[\[Zeta]] = 3;
B[\[Zeta]] = 4;

list1 = {A, B};
list2 = {10*\[Psi], 5 \[Phi] + \[Zeta]};

list3 = Table[Table[i[First@Variables[j]], {i, list1}], {j, list2}]

which gives as the output the desired answer

{{1, 2}, {3, 4}}