Mecnica Quntica

Carlos Eduardo AguiarCarlos Eduardo Aguiar

Programa de Ps-Graduao em Ensino de FsicaInstituto de Fsica - UFRJ

1 perodo letivo, 2014

Ensino e aprendizagem de mecnica quntica

Dificuldades conceituais Superposio quntica

Probabilidade subjetiva x objetiva

Complementaridade

O problema da medida

Realismo vs. localidade Realismo vs. localidade

Dificuldades matemticas Vetores

Nmeros complexos

Espaos vetoriais complexos

Operadores, autovalores, autovetores

Dimenso infinita, operadores diferenciais, funes especiais

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Sobre o ensino e aprendizagem de mecnica quntica

D. F. Styer, Common misconceptions regarding quantum mechanics, American Journal of Physics 64 , 31, 1996.

I. D. Johnston, K. Crawford, P. R. Fletcher, Student difficulties in learning quantum mechanics, International Journal of Science Education 20 , 427, 1998.

S. Vokos, P. S. Shaffer, B. S. Ambrose, L. C. McDermott, Student understanding of the wave nature of matter: Diffraction and interference of particles, American Journal of Physics 68, S42, 2000.

G. Ireson, The quantum understanding of pre-university physics students, Physics Education 35, 15, 2000.

M. A. Moreira, I. M. Greca, Uma reviso da literatura sobre estudos relativos ao ensino da mecnica quntica introdutria, Investigaes em Ensino de Cincias 6, 29, 2001.

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mecnica quntica introdutria, Investigaes em Ensino de Cincias 6, 29, 2001. I. M. Greca, M. A. Moreira, V.E. Herscovitz, Uma proposta para o ensino de mecnica quntica,

Revista Brasileira de Ensino de Fsica 33, 444, 2001.

C. Singh, Student understanding of quantum mechanics, American Journal of Physics 69, 885, 2001. E. Cataloglu, R. W. Robinett, Testing the development of student conceptual and visualization

understanding in quantum mechanics through the undergraduate career, American Journal of Physics 70, 238, 2002.

K. Mannila, I. T. Koponen, J. A. Niskanen, Building a picture of students conceptions of wave- and particle-like properties of quantum entities, European Journal of Physics 23, 45, 2002.

R. Mller, H. Wiesner, Teaching quantum mechanics on an introductory level, American Journal ofPhysics 70, 200, 2002; ver tambm Am. J. Phys. 70, 887, 2002.

Sobre o ensino e aprendizagem de mecnica quntica

I. M. Greca, O. Freire Jr, Does an emphasis on the concept of quantum states enhance students understanding of quantum mechanics?, Science & Education 12 , 541, 2003.

F. Ostermann, T. F. Ricci, Construindo uma unidade didtica conceitual sobre mecnica quntica: um estudo na formao de professores de fsica, Cincia & Educao 10, 235, 2004.

D. T. Brookes, E. Etkina, Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning, Physical Review Special Topics - Physics Education Research 3, 010105, 2007.

S. B. McKagan, K. K. Perkins, C. E. Wieman, Why we should teach the Bohr model and how to teach it effectively, Physical Review Special Topics - Physics Education Research 4, 10103, 2008.

C. Singh, Student understanding of quantum mechanics at the beginning of graduate instruction, American Journal of Physics 76, 277, 2008.

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C. Singh, Student understanding of quantum mechanics at the beginning of graduate instruction, American Journal of Physics 76, 277, 2008.

C. Singh, Interactive learning tutorials on quantum mechanics, American Journal of Physics 76, 400, 2008.

L. D. Carr, S. B. McKagan, Graduate quantum mechanics reform, American Journal of Physics 77, 308, 2009.

M. Dubson, S. Goldhaber, S. Pollock, K. Perkins, Faculty Disagreement about the Teaching of Quantum Mechanics, 2009 Physics Education Research Conference, AIP Conference Proceedings 1179, 137, 2009.

C. Baily, N. D. Finkelstein, Development of quantum perspectives in modern physics, Physical Review Special Topics - Physics Education Research 5, 10106, 2009.

C. Baily, N. D. Finkelstein, Teaching and understanding of quantum interpretations in modern physics courses, Physical Review Special Topics - Physics Education Research 6, 10101, 2010.

Sobre o ensino e aprendizagem de mecnica quntica

S. B. McKagan, K. K. Perkins, C. E. Wieman, Design and validation of the Quantum Mechanics Conceptual Survey, Physical Review Special Topics - Physics Education Research 6, 020121, 2010.

L. Deslauriers, C. E. Wieman, Learning and retention of quantum concepts with different teaching methods, Physical Review Special Topics - Physics Education Research 7, 010101, 2011.

M. Ayene, J. Kriek, B. Damtie, Wave-particle duality and uncertainty principle: Phenomenographiccategories of description of tertiary physics students depictions, Physical Review Special Topics -Physics Education Research 7, 020113, 2011.

G. Zhu, C. Singh, Improving students understanding of quantum mechanics via the SternGerlachexperiment, American Journal of Physics 79, 499, 2011.

G. Zhu, C. Singh, Improving students understanding of quantum measurement. I. Investigation of

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G. Zhu, C. Singh, Improving students understanding of quantum measurement. I. Investigation of difficulties, Physical Review Special Topics - Physics Education Research 8, 101117, 2012.

G. Zhu, C. Singh, Improving students understanding of quantum measurement. II. Development of research-based learning tools, Physical Review Special Topics - Physics Education Research 8, 101118, 2012.

O. Levrini, P. Fantini, Encountering Productive Forms of Complexity in Learning Modern Physics, Science & Education 22,1895, 2013.

A. Kohnle et al., A new introductory quantum mechanics curriculum, European Journal of Physics 35, 015001, 2014.

J. Castrillon, O. Freire Jr, B. Rodriguez, Mecnica cuntica fundamental, una propuesta didctica, Revista Brasileira de Ensino de Fsica 36, 1505, 2014.

Leituras recomendadas

R. P. Feynman, R. B. Leighton, M. Sands, Lies de Fsica de Feynman, vol. III, Bookman, 2008. R. P. Feynman, QED - A estranha teoria da luz e da matria, Gradiva, 1988. H. M. Nussenzveig, Curso de Fsica Bsica: tica, Relatividade, Fsica Quntica, Blucher, 2002. O. Pessoa Jr, Conceitos de Fsica Quntica, Livraria da Fsica, 2003. A. Zeilinger, A Face Oculta da Natureza, Globo, 2005. M. Le Bellac, The Quantum World, World Scientific, 2013. T. Hey, P. Walters, The New Quantum Universe, Cambridge UP, 2003. V. Scarani, Quantum physics: a first encounter, Oxford UP, 2006. B. Rosenblum , F. Kuttner , Quantum Enigma: Physics Encounters Consciousness, Oxford UP,

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B. Rosenblum , F. Kuttner , Quantum Enigma: Physics Encounters Consciousness, Oxford UP, 2006.

L. Susskind, A. Friedman, Quantum Mechanics: The Theoretical Minimum, Basic Books, 2014 A. Rae, Quantum Physics: Illusion or Reality?, Cambridge UP, 2012. J. Polkinghorne, Quantum Theory: A Very Short Introduction, Oxford UP, 2002. D. F. Styer, The Strange World of Quantum Mechanics, Cambridge UP, 2000. D. McIntyre, C. A. Manogue, J. Tate, Quantum Mechanics: A Paradigms Approach, Addison-

Wesley, 2012.

M. Le Bellac, Quantum Physics, Cambridge UP, 2006.

Simulaes

Interfermetro de Mach-Zehnder (Universidade Federal do Rio Grande do Sul)http://www.if.ufrgs.br/~fernanda/

Experincia de Stern-Gerlach (Universidade Federal do Rio Grande do Sul)http://www.if.ufrgs.br/~betz/quantum/SGtexto.htm

QuantumLab (Universitt Erlangen-Nrnberg)http://www.didaktik.physik.uni-erlangen.de/quantumlab/english/index.html

PhET (University of Colorado)http://phet.colorado.edu/pt_BR/simulations/category/physics/quantum-phenomena

SPINS (Oregon State University)http://www.physics.orst.edu/~mcintyre/ph425/spins/index_SPINS_OSP.html

Quantum physics (cole Polytechnique)http://www.quantum-physics.polytechnique.fr/index.html

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Internet

Quantum Physics (IoP)http://quantumphysics.iop.org/

Quantum Mechanics (Leonard Susskind)http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter

Quantum Entanglement (Leonard Susskind) Quantum Entanglement (Leonard Susskind)http://theoreticalminimum.com/courses/quantum-entanglement/2006/fall

Advanced Quantum Mechanics (Leonard Susskind)http://theoreticalminimum.com/courses/advanced-quantum-mechanics/2013/fall

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Sumrio

1. Fenmenos qunticos

2. Princpios da mecnica quntica

3. Sistemas qunticos simples: aplicaes

4. Realismo, contextualidade e no-localidade

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5. Partculas idnticas

6. Operadores, autovalores e autovetores

7. Simetrias

8. Posio e momentum

9. Partcula em uma dimenso

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