플랑크-아인슈타인 관계식

플랑크-아인슈타인 관계식(Planck-Einstein relation)[1][2][3] 또는 플랑크의 에너지-주파수 관계식(Planck's energy-frequency relation)은[4] 양자역학의 기본적인 공식 중 하나로, 광자에너지 가 그 진동수 에 비례한다는 내용을 담고 있다.

이때 비례상수 플랑크 상수라 한다. 같은 관계를 광자의 각진동수 를 써서 나타낼 수도 있다.

이때 이다. 플랑크-아인슈타인 관계식은 빛의 양자적 성질을 설명해 주며, 광전 효과흑체 복사와 같은 현상을 이해하는 데 핵심적인 역할을 한다.

분광 형태

전자기파로서의 빛은 분광적인 물리량을 이용해 특정지어질 수 있다. 여기서 분광적인 물리량은 진동수 , 파장 , 파수 (또는 이에 대응하는 각물리량인 각진동수 , 각파장 , 각파수 )와 같은 것을 말한다.

이러한 요소들은 다음과 같은 관계를 갖고 있다.

이에 따른 플랑크 관계식의 ‘표준 형태’는 다음과 같다.

‘각 형태’는 다음과 같다.

이때 빛의 속도를 나타낸다.

드 브로이 관계식

드 브로이 관계식[5][6][7] 또는 드 브로이 운동량-파장 관계식은[4] 플랑크 관계식을 일반화하여 물질파에 적용한 형태이다. 이 식은 다음과 같다.

또는

이를 벡터 형태로 바꾸면 다음과 같다.

이때 는 운동량 벡터, 는 각파동 벡터이다.

같이 보기

각주

  1. French & Taylor (1978), pp. 24, 55.
  2. Cohen-Tannoudji, Diu & Laloë (1973/1977), pp. 10–11.
  3. Kalckar 1985, p. 39.
  4. Schwinger (2001), p. 203.
  5. Weinberg (1995), p. 3.
  6. Messiah (1958/1961), p. 14.
  7. Cohen-Tannoudji, Diu & Laloë (1973/1977), p. 27.

참고 문헌

  • Cohen-Tannoudji, C., Diu, B., Laloë, F. (1973/1977). Quantum Mechanics, translated from the French by S.R. Hemley, N. Ostrowsky, D. Ostrowsky, second edition, volume 1, Wiley, New York, ISBN 0471164321.
  • French, A.P., Taylor, E.F. (1978). An Introduction to Quantum Physics, Van Nostrand Reinhold, London, ISBN 0-442-30770-5.
  • Griffiths, D.J. (1995). Introduction to Quantum Mechanics, Prentice Hall, Upper Saddle River NJ, ISBN 0-13-124405-1.
  • Landé, A. (1951). Quantum Mechanics, Sir Isaac Pitman & Sons, London.
  • Landsberg, P.T. (1978). Thermodynamics and Statistical Mechanics, Oxford University Press, Oxford UK, ISBN 0-19-851142-6.
  • Messiah, A. (1958/1961). Quantum Mechanics, volume 1, translated from the French by G.M. Temmer, North-Holland, Amsterdam.
  • Schwinger, J. (2001). Quantum Mechanics: Symbolism of Atomic Measurements, edited by B.-G. Englert, Springer, Berlin, ISBN 3-540-41408-8.
  • van der Waerden, B.L. (1967). Sources of Quantum Mechanics, edited with a historical introduction by B.L. van der Waerden, North-Holland Publishing, Amsterdam.
  • Weinberg, S. (1995). The Quantum Theory of Fields, volume 1, Foundations, Cambridge University Press, Cambridge UK, ISBN 978-0-521-55001-7.
  • Weinberg, S. (2013). Lectures on Quantum Mechanics, Cambridge University Press, Cambridge UK, ISBN 978-1-107-02872-2.
  • Flowers, P., Theopold,K., Langley, R. (n.d.). Chemistry, chapter 6, Electronic Structure and Periodic Properties of Elements, OpenStax, https://opentextbc.ca/chemistry/chapter/6-2-the-bohr-model/ Archived 2021년 5월 6일 - 웨이백 머신.

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