VI.Review on basic concepts in quantum mechanics I.INTRODUCTION:MATTER WAVE AND ITS MOTION The emergence and development of quantum mechanics began in early years of the pre- vious century and accomplished at the end of the twentieth years of the same century.We will not trace the historical steps since it is a long story.Here we try to access the theory by a way that seems to be more "natural"and more easily conceivable. A.de Broglie's hypothesis Inspiration:Parallelism between light and matter Wave:frequency,w,wavelength入，wave vectork.… Particle:velocity v,momentum p,energy s...... .Light is traditionally considered to be a typical case of wave.Yet,it also shows (possesses)a corpuscle nature-light photon.For monochromatic light wave e=hv=hw g-费林，k=贸 .Matter particles should also possess another side of nature-the wave nature e=hv=hw P=1=k This is call de Broglie's Hypothesis and is verified by all experiments.In the case of non-relativistic theory,the de Broglie wavelength for a free particle with mass m and energy e is given by 入=h/p=h/W2me The state of (micro)-particle should be described by a wave function.Here are some examples of state functions: 3VI. Review on basic concepts in quantum mechanics 36 I. INTRODUCTION: MATTER WAVE AND ITS MOTION The emergence and development of quantum mechanics began in early years of the pre￾vious century and accomplished at the end of the twentieth years of the same century. We will not trace the historical steps since it is a long story. Here we try to access the theory by a way that seems to be more ”natural” and more easily conceivable. A. de Broglie’s hypothesis Inspiration: Parallelism between light and matter Wave: frequency ν, ω, wavelength λ, wave vector k · · · · · · Particle: velocity v, momentum p, energy ε · · · · · · • Light is traditionally considered to be a typical case of wave. Yet, it also shows (possesses) a corpuscle nature - light photon. For monochromatic light wave ε = hν = ~ω p = hν c = h λ = ~k, (k = 2π λ ) • Matter particles should also possess another side of nature - the wave nature ε = hν = ~ω p = h λ = ~k This is call de Broglie’s Hypothesis and is verified by all experiments. In the case of non-relativistic theory, the de Broglie wavelength for a free particle with mass m and energy ε is given by λ = h/p = h/√ 2mε The state of (micro)-particle should be described by a wave function. Here are some examples of state functions: 3