B. R. MU 31

where

22 32

11 11

and 12

rna r

na

(3.8)

Finally, we obtain the modified energy spectra of hy-

drogen atom that

2

2

00

,, 2

0

02

,, ,2

32

0

00

2

0

22

2

2

2

2

3

1

24

41

1

42

2

14

18

2

2

+4m12

nn

ns n

nn

n

e

EE na

EEm e

sna

b

Em E

na

b

mE

na

m

b

sn

2

a

(3.9)

When n is large enough, in our introduction before,

will gives us . But, we obtain new value in here

when n is large, the spectra is

0

n

E

22

,,02

12 2

n

Em

2

(3.10)

This result is too surprised. As we known, the usual

ground state of hydrogen atom is. With energy

level increase, the value of energy go up to, however,

specially, there exits the upper bound when is large

enough which equals zero. But, our result introduction

the new spectra of hydrogen atom when n is large. Above

the upper bound, we find new spectra! This result is not

end of journey, noteworthily, as our works before, we

have the relations

13.6eV

n

in Planck scale. It express

that

2

2

,,0 2

12 2

n

Em

(3.11)

which is the energy spectra of extra dimension. Consid-

ering the physical meaning of the nonzero position dis-

tance in Planck scale, there exists the minimal black hole

and the horizon is that nonzero po int. This condition lead

the hydrogen atom has unbounded state in extra dimen-

sions and which is reason that we obtain the positive

spectra in final.

4. Summary

We use GUP and extra dimensions models to rewritten

the equation of hydrogen atom and obtain the modified

energy spectra which is far from the familiar solution that

has a upper bound. In this modified spectra, we find that

there also exits discrete spectra in field of >0

, which

is same as the free particle that lives in extra dimensions.

This result is not familiar in usual hydrogen atom. As this

term is contributed by the wave function in extra dimen-

sion, it introduces the new method to find extra dimen-

sions in intermediate energy scale.

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