Find the solution of Det[Matrix]==0?

Questions
1

How to find the solution of Det[Matrix]==0? Details of the matrix are appended below.

potential well.nb (10.2 KB)

2

Solve for what?
In[12]:= matr = {{0, 1, -1, 0}, {k, 0, -[Alpha], 0}, {Sin[k a],
Cos[k a], 0,
e^-[Alpha]a}, {k Cos[k a], -k Sin[k a], -[Alpha]e^-[Alpha]a,
0}};
MatrixForm[matr1]
Det[matr] == 0

Out[13]//MatrixForm= !(
TagBox[
RowBox[{“(”, “”, GridBox[{
{“0”, “1”,
RowBox[{“-”, “1”}], “0”},
{“k”, “0”,
RowBox[{“-”, “[Alpha]”}], “0”},
{
RowBox[{“Sin”, “[”,
RowBox[{“a”, " “, “k”}], “]”}],
RowBox[{“Cos”, “[”,
RowBox[{“a”, " “, “k”}], “]”}], “0”,
SuperscriptBox[“e”,
RowBox[{”-”, “[Alpha]a”}]]},
{
RowBox[{“k”, " “,
RowBox[{“Cos”, “[”,
RowBox[{“a”, " “, “k”}], “]”}]}],
RowBox[{
RowBox[{”-”, “k”}], " “,
RowBox[{“Sin”, “[”,
RowBox[{“a”, " “, “k”}], “]”}]}],
RowBox[{”-”,
SuperscriptBox[“[Alpha]e”,
RowBox[{“-”, “[Alpha]a”}]]}], “0”}
},
GridBoxAlignment->{“Columns” → {{Center}}, “Rows” → {{Baseline}}},
GridBoxSpacings->{“Columns” → {
Offset[0.27999999999999997], { Offset[0.7]}, Offset[0.27999999999999997]}, “Rows” → {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}}], “”, “)”}],
Function[BoxForme$, MatrixForm[BoxForme$]]])

Out[14]= -e^-[Alpha]a k [Alpha]e^-[Alpha]a +
e^-[Alpha]a k [Alpha] Cos[a k] - e^-[Alpha]a k^2 Sin[a k] == 0

3

Thank you Virbhadra

4

There are 3 variables in your equation. 2 of them must be known to get 3rd one.
Use NSolve command to do that.
Are you student of Dr. R. C. Srivastava? He was there at Gorakhpur University.