Transcription of QUANTUM MECHANICS I - Physics and Astronomy …
1 1 QUANTUM MECHANICS PLANCK AND EINSTEIN LIGHT WAVE LIKE PARTICLE LIKE de BROGLIE PARTICLES PARTICLE LIKE WAVE LIKE ??? 2 CONSIDER WAVE )(2sin),(ftxtx or )sin(),(tkxtx where 2k f 2 3 CAN DEFINE and f NOTE THE NODES ARE MOVING WHERE ARE NODES? 40)sin( tkx or ntkx so ktnx DIFERENTIATE wrt t 5ffkdtdx /22 THIS IS THE PHASE VELOCITY vph 6 ADDITION OF WAVES 7 MATH ADDITION OF WAVES Add two waves ),(),(),(21txtxtx t)-sin(kx=t)(x, 1 and tdxdkktx)(sin),(2 USE )(21sin)(21cos2sinsinBABABA 8TO GET tdxdkkdxdktx2222sin)22cos(2),( BUT dk<<k and d << SO )sin(22cos2),(tkxtdxdktx 9 GROUP VELOCITY dkddkdvg 2/2/ 10 THEN ADD SEVEN WAVES TO GET
