因為缺乏完整的量子重力，霍金輻射的研究大多還是無法掌握黑洞蒸發的最後階段。本論文的目的是為了增進二簡諧振子模型的新分析用以幫助了解黑洞蒸發相的現象。考慮在類比黑洞的簡諧振子所帶有的負勢能來模擬黑洞帶有的負比熱的不穩定性。我們不僅討論黑洞及霍金輻射的可能演化並且還討論黑洞與霍金輻射的總量子態的演化。

Research on Hawking radiation often fails to grasp the ¯nal stage of black hole evaporation because of lacking full quantum gravity. The purpose of this thesis is to advance a new analysis with the model of two harmonic oscillators to help to understand the phenomenon of the evaporation phase of the black hole. It is very important to consider the negative potential energy in the harmonic oscillator analogue of the black hole to simulate instability of the black hole with negative speci¯c heat. We not only discuss possible evolutions of the black hole and Hawking radiation but also the evolution of the total state of the black hole and Hawking radiation.

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