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本文提出了一个描述金融投资项目演化的量子力学状态方程，该方程的参数比较好地模拟了金融市场的基本要素，包括投资（输入）、资产损耗（缩水）、资产增益、和收益（输出）等，方程中的量子力学算符也能够反映该项目的动力学过程与特征，所以能代表一类金融投资项目（其状态用Dirac符号表示）在市场中的演化模式. 通过引入纠缠态表象得出了该方程的量子解（算符之和形式），该量子解给出了初态与终态的联系，也就给出了投资项目的动态过程. 作为例子，求出单一投资项目在金融市场中的演化，不但得出了符合市场演化趋势的解，而且提出了二项-负二项纠缠态. 在推导过程中，充分利用了Dirac符号和有序算符内的积分技术（IWOP）.This paper proposes a quantum mechanical state equation for describing evolution of projects of financial investment, while the parameters of this equation well simulate the fundamental elements of financial market, including investment (input), assets loss (assets decrease), assets increase and income (output), the quantum mechanics operators involved in this equation also can reflect the dynamic process and characteristics of the project, so the equation can be taken as the evolution model of a kind of financial investment projects in the market. The entangled state representation is introduced to solve this equation and its solution is obtained in an infinite operator-sum form, which exhibits the link between the initial state and final state, i.e., the dynamic process of the financial investment project. As an example, we derive the evolution law of a pure investment project in financial market, which conforms with the evolution trend of the market. In solving the equation we also find a new state which we name it as the binomial-negative binomial entangled state. Throughout the discussions we make full use of Dirac's symbolic method and the technique of integration within an ordered product (IWOP) of operators.
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Keywords:
- econophysics /
- evolution of project of financial investment /
- binomial-negative-binomial entangled state /
- entangled state representation
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[10] Mishkin F S 2012 The Economics of Money, Banking and Financial Markets (Prentice Hall)
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[12] Wang C C, Fan H Y 2012 Int. J. Theor. Phys. 51 193
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[15] Fan H Y, Fan Y 1996 Phys. Rev. A 54 958
[16] Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
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[1] Mantegna R N, Stanley H E 2007 An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press)
[2] Johnson N F, Jefferies P, Hui P M 2003 Financial Market Complexity: What Physics can Tell us about Market Behaviour (Oxford University Press)
[3] McCauley J L, Gunaratne G H, Bassler K E 2007 Physica. A 379 1
[4] Zhou W X 2007 An Introduction to Econophysics (Shanghai: Shanghai University of Finance and Economics Press) (in Chinese) [周炜星 2007 金融物理学导论(上海:上海财经大学出版社)]
[5] Huang J P 2013 Econophysics (Beijing: Higher Education Press) (in Chinese) [黄吉平 2013 经济物理学(北京:高等教育出版社)]
[6] Huang Z G, Chen Y, Zhang Y, Wang Y H 2007 Chin. Phys. B 16 975
[7] Xin B G, Liu Y Q, Chen T 2011 Acta Phys. Sin. 60 048901 (in Chinese) [辛宝贵, 刘艳芹, 陈通 2011 物理学报 60 048901]
[8] Wang Y G, Guo L P 2010 Physics. 39 85 (in Chinese) [王有贵, 郭良鹏 2010 物理 39 85]
[9] Baaquie B E 2007 Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates (Cambridge University Press)
[10] Mishkin F S 2012 The Economics of Money, Banking and Financial Markets (Prentice Hall)
[11] Samuelson P A 2009 Economics (McGraw Hill Higher Education)
[12] Wang C C, Fan H Y 2012 Int. J. Theor. Phys. 51 193
[13] Fan H Y, Hu L Y 2008 Mod. Phys. Lett. B 25 2435
[14] Fan H Y, Hu L Y 2009 Chin. Phys. B 18 1061
[15] Fan H Y, Fan Y 1996 Phys. Rev. A 54 958
[16] Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
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