ID 110908
Author
Content Type
Departmental Bulletin Paper
Description
In this paper, we study the phenomena of potential well of infinite depth on the view point of natural statistical physics. The mathematical model of this physical system is the system of micro-particles moving periodically with constant velocity in the interval D = [−a, a], (a > 0).
Thereby we obtain the structure of this physical system at the stationary state.
Thus we clarify that this physical system is the composed state of the proper physical systems at the stationary state and the ratio of their composition is given by the sequence

{|an|2}n=0 ∪ {|bn|2}∞n=1,

where an, (n ≥ 0) and bn, (n ≥ 1) are the Fourier type coefficients of the initial state ψ ∈ L2.
Then we obtain the energy expectation of the total physical system
     
Ē =∞Σn=0 n2π2ℏ2/2ma2 (|an|2 + |bn|2),
     
where m denotes the mass of one micro-particle.
Journal Title
Journal of Mathematics
ISSN
13467387
NCID
AA11595324
Volume
49
Start Page
59
End Page
77
Sort Key
59
Published Date
2015
FullText File
language
eng
TextVersion
Publisher
departments
Science and Technology