以量纲分析重新发现普朗克公式
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摘要
本研究以量纲分析手法,完全独立于普朗克研究黑体辐射的物理图像,更不用普朗克常数,就能推导出黑体辐射公式,展现量纲分析的工具优势。过程会辅以一个扩充基本量、二项特征假设、三处属性拟合、四条辐射方程、五道抉择关卡,从经典物理范畴开始,考量能量量纲在时空作用下诱导出必要的物理基本常数,接着采用Π定理算出两个无量纲量并建立其Π函数关系式,然后运用自创的属性拟合法,辐射公式的形式就自动浮显出来,最后导出黑体辐射公式,并证明与普朗克公式等价。
This work represents an approach using dimensional analysis to rediscover the Planck's formula.Without using the Planck's constant we obtain the quantitative black-body radiation laws by calculating directly energy density function based on the Buckingham'sΠtheorem.By means of numerical analysis,we can also derive the Stefan-Boltzmann law and Wien's displacement law.These derivations were straightforward and only based on a simple assumption of an equivalent constant.
This work represents an approach using dimensional analysis to rediscover the Planck's formula.Without using the Planck's constant we obtain the quantitative black-body radiation laws by calculating directly energy density function based on the Buckingham'sΠtheorem.By means of numerical analysis,we can also derive the Stefan-Boltzmann law and Wien's displacement law.These derivations were straightforward and only based on a simple assumption of an equivalent constant.
引文
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[5]邓崇林.以简明物理法重新发现巴耳末公式[J].物理与工程,2019,29(1):44-52.TENG C L.A concise approach in physics reforms Balmer's formula[J].Physics and Engineering,2019,29(1):44-52.(in Chinese)
[6]邓崇林,创新量纲分析重导玻尔模型能级公式[J],物理与工程,2019,29(2):41-46.TENG C L.Using new approach in dimensional analysis to reform the formula for the Bohr model's energy levels[J].Physics and Engineering,2019,29(2):41-46.(in Chinese)
[7]李海,赵玉生.量子物理学的基石[J].物理,2001,30(11):724-728.LI H,ZHAO Y S.The corner stone of quantum physics[J].Physics,2001,30(11):724-728.(in Chinese)
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[9]张三慧.大学物理学:量子物理.第五册[M].北京:清华大学出版社,2000:5.
[10]林琦焜.从量纲看世界[J].数学传播,2009,33(3):13-27.LIN C K.The uses of dimensional analysis to describe the world[J].Mathmedia,2009,33(3):13-27.(in Chinese)
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[12]PATHRIA R K.Statistical physics[M].Pergamon Press,1972:502-504.
[13]GREINER W.Quantum mechanics:An introduction[M].Springer,2012:21.
[14]IRWIN J A.Astrophysics:Decoding the cosmos[M].John Wiley&Sons,2007:130.
[15]VANDERWERF D F.The story of light science[M].Springer,2017:320.
[16]CRAWLEY G M.The world scientific handbook of energy[M].World Scientific,2013:512.
[17]向梅,李梓兮,马晓栋.维恩位移定律的剖析[J].新疆师范大学学报(自然科学版),2015,34(3):44-47.XIANG M,LI Z X,MA X D.Analysis of Wien displacement law[J].Journal of Xinjiang Normal University(Natural Sciences Edition),2015,34(3):44-47.(in Chinese)
[18]MEHRA J,RECHENBERG H.The historical development of quantum theory[M].Springer,2000:74.
[19]赵凯华.定性与半定量物理学[M].北京:高等教育出版社,1991:86-87.
[20]孙博华.量纲分析以及应用[J].物理与工程,2016,26(6):3-12.SUN B H.Dimensional analysis and applications[J].Physics and Engineering,2016,26(6):3-12.(in Chinese)
[21]黃永义.普朗克黑体辐射定律的建立过程[J].广西物理,2011,32(3):32-36.HUANG Y Y.Establishing the Planck's radiation law[J].GuangXi Physics,2011,32(3):32-36.(in Chinese)
[2]LONGAIR M.Theoretical concepts in physics:An alternative view of theoretical reasoning in physics[M].Cambridge University Press,2003:297.
[3]BELLONI M,CHRISTIAN W,COX A J.Physlet quantum physics:An interactive introduction[M].Prentice Hall,2006:35.
[4]向义和.大学物理导论:物理学的理论与方法、历史与前沿[M].北京:清华大学出版社,1999:258-259.
[5]邓崇林.以简明物理法重新发现巴耳末公式[J].物理与工程,2019,29(1):44-52.TENG C L.A concise approach in physics reforms Balmer's formula[J].Physics and Engineering,2019,29(1):44-52.(in Chinese)
[6]邓崇林,创新量纲分析重导玻尔模型能级公式[J],物理与工程,2019,29(2):41-46.TENG C L.Using new approach in dimensional analysis to reform the formula for the Bohr model's energy levels[J].Physics and Engineering,2019,29(2):41-46.(in Chinese)
[7]李海,赵玉生.量子物理学的基石[J].物理,2001,30(11):724-728.LI H,ZHAO Y S.The corner stone of quantum physics[J].Physics,2001,30(11):724-728.(in Chinese)
[8]钱学森.写在前面(序)-土岩爆破文集(全国工程爆破学术会议论文选)[C].1980.
[9]张三慧.大学物理学:量子物理.第五册[M].北京:清华大学出版社,2000:5.
[10]林琦焜.从量纲看世界[J].数学传播,2009,33(3):13-27.LIN C K.The uses of dimensional analysis to describe the world[J].Mathmedia,2009,33(3):13-27.(in Chinese)
[11]秦克诚.邮票上的物理学史[M].北京:清华大学出版社,2005:199.
[12]PATHRIA R K.Statistical physics[M].Pergamon Press,1972:502-504.
[13]GREINER W.Quantum mechanics:An introduction[M].Springer,2012:21.
[14]IRWIN J A.Astrophysics:Decoding the cosmos[M].John Wiley&Sons,2007:130.
[15]VANDERWERF D F.The story of light science[M].Springer,2017:320.
[16]CRAWLEY G M.The world scientific handbook of energy[M].World Scientific,2013:512.
[17]向梅,李梓兮,马晓栋.维恩位移定律的剖析[J].新疆师范大学学报(自然科学版),2015,34(3):44-47.XIANG M,LI Z X,MA X D.Analysis of Wien displacement law[J].Journal of Xinjiang Normal University(Natural Sciences Edition),2015,34(3):44-47.(in Chinese)
[18]MEHRA J,RECHENBERG H.The historical development of quantum theory[M].Springer,2000:74.
[19]赵凯华.定性与半定量物理学[M].北京:高等教育出版社,1991:86-87.
[20]孙博华.量纲分析以及应用[J].物理与工程,2016,26(6):3-12.SUN B H.Dimensional analysis and applications[J].Physics and Engineering,2016,26(6):3-12.(in Chinese)
[21]黃永义.普朗克黑体辐射定律的建立过程[J].广西物理,2011,32(3):32-36.HUANG Y Y.Establishing the Planck's radiation law[J].GuangXi Physics,2011,32(3):32-36.(in Chinese)