Abstract
Expressions for critical temperature of Bose-Einstein condensation (BEC) in an e xternal potential, which are different from published results in the literatur e, are presente d. The results reveal the relation between the critical temperature of BECgas and the external potential, and demonstrates proporti onality of critical temperature in external potential to the value T0c at which th e potential is absent. In addition, a criterion for the validity of potential is also prese nted, which is based on the comparison between the potential and the product kT 0c. This comparison shows that only when the external potential is nearly eq ual to or larg er than kT0c, the increase of critical temperature is significant. A s the potential is much smaller than kT０c, the potential has no effects on the BEC gas.
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