Question

How is degeneracy of a particle in a box equal to 2?

Answer 1

So I was reading this book which introduces degeneracy as the states having same Energy.

Consider the case of particle in a 2D square box.

In such case, the wave function is

Now both E1,2 E2,1 are same so these are degenerate orbitals and the degeneracy is 2.

Further it states that degeneracy for Particle in Box is at most two.

But let us consider the following three cases:

n1 = 10, n2 = 10

n1 = 14, n2 = 2

n1 = 2, n2 = 14

In all the three cases mentioned, the energy of the particle would be

200E. Where E is a known constant made up of planck's constant, mass of particle and Length of the square box.

Extending the same argument further, one can't say what the maximum degeneracy of particle in a box of n dimensions unless the energy level is already given. For very high energy levels, there would be a lot of cases where you can represent a number in 2 different ways as square of two naturals.

I do not know where I am going wrong. Is there a flaw in the way I understood Degeneracy?

Edit Adding another picture of the text from the same book.