Hi Aydin Amini;

In two dimensional hydrogen atom (2D) the main quantum number starts from zero and so it has zero point energy whereas in three dimensional hydrogen (3D) the main quantum number starts from one and it has no zero point energy. Also in 3D the binding energy of excited ground state is E0 but in 2D it is 4E0. So the large binding energy in 2D can be understood by decreasing the width of quantum well structure.

Best regards

Dear professor ;

Thanks for your attention

Actually in my reference, and also in all others, the quantum number started from 1 (i.e. n=1)

S.L.Chung, "physics of photonic devices” - page 96 and 97

and we have nonzero ground-state. Anyway, the concept of diminishing the QW size result in higher binding energy is reasonable.

regards,

Amini

Dear Aydin,

you asked na interesting question. I found a Bachelor's thesis, where this question is discussed (see attachement).

The solution of this problem almost is formed in classical electrodynamic. The solution of the Poisson equation gives a potential in D > 2 dimensions as ß*r 2-D and for D = 2 a potential ß*ln(r) with r the distance. The solution of the ground state energy is plotted at page 9 as you wrote. (Sorry, the text is german but the calculations can be understood).

With regard

R. Mitdank