mDB = (({{α - ϵ, β, 0, β, 0, β}, {β, α - ϵ, β, 0, 0, 0}, {0, β, α - ϵ, β, 0, 0}, {β, 0, β, α - ϵ, β, 0}, {0, 0, 0, β, α - ϵ, β}, {β, 0, 0, 0, β, α - ϵ}}))

solDB = Solve[Det[mDB] == 0, ϵ]

fDB = ϵ/.solDB

ϵPiDB = Simplify[2 fDB[[6]] + 2 fDB[[2]] + 2 fDB[[5]]]

ϵPiDBges = N[ϵPiDB ]

mBz = (({{α - ϵ, β, 0, 0, 0, β}, {β, α - ϵ, β, 0, 0, 0}, {0, β, α - ϵ, β, 0, 0}, {0, 0, β, α - ϵ, β, 0}, {0, 0, 0, β, α - ϵ, β}, {β, 0, 0, 0, β, α - ϵ}}))

solBz = Solve[Det[mBz] == 0, ϵ]

fBz = ϵ/.solBz

ϵPiBz = Simplify[2 fBz[[6]] + 2 fBz[[5]] + 2 fBz[[4]]]

ϵPiBzges = N[ϵPiBz ]

Simplify[ϵPiDBges - ϵPiBzges]

fDB[[1]]

sDB1 = mDB/.ϵ-> fDB[[1]]

cvDB1 = NullSpace[sDB1][[1]]

sDB2 =  mDB/.ϵ-> fDB[[2]]

cvDB2 = NullSpace[sDB2][[1]]

sDB3 = mDB/.ϵ-> fDB[[3]]

cvDB3 = NullSpace[sDB3][[1]]

sDB4 =mDB/.ϵ-> fDB[[4]]

cvDB4 = NullSpace[sDB4][[1]]

sDB5 = mDB/.ϵ-> fDB[[5]]

cvDB5 = NullSpace[sDB5][[1]]

sDB6 = mDB/.ϵ-> fDB[[6]]

cvDB6 = NullSpace[sDB6][[1]]

cvDB1n = cvDB1 / (Sqrt[(cvDB1.cvDB1)])

cvDB2n = cvDB2 / (Sqrt[(cvDB2.cvDB2)])

cvDB3n = cvDB3 / (Sqrt[(cvDB3.cvDB3)])

cvDB4n = cvDB4 / (Sqrt[(cvDB4.cvDB4)])

cvDB5n = cvDB5 / (Sqrt[(cvDB5.cvDB5)])

cvDB6n = cvDB6 / (Sqrt[(cvDB6.cvDB6)])

cvDB1n.cvDB1n

cvDB2n.cvDB2n

cvDB3n.cvDB3n

cvDB4n.cvDB4n

cvDB5n.cvDB5n

cvDB6n.cvDB6n

cvDB1n.cvDB2n

cvDB1n.cvDB3n

cvDB1n.cvDB4n

cvDB1n.cvDB5n

cvDB1n.cvDB6n

cvDB2n.cvDB3n

cvDB2n.cvDB4n

cvDB2n.cvDB5n

cvDB2n.cvDB6n

cvDB3n.cvDB4n

cvDB3n.cvDB5n

cvDB3n.cvDB6n

cvDB4n.cvDB5n

cvDB4n.cvDB6n

cvDB5n.cvDB6n