504 Quantum Mechanics*P41.37(a)For the center of mass to be fixed, mv11220+=. Thenvv v vmmvmmmv=+=+=+1211212121and v1212=+. Similarly, vmmvv=+21andv21=+. Then12121212121212121212222212 122kxmmvkxmm mmvkxx++=++++=+++=+bgµ(b)ddxx12120+FHGIKJ=because energy is constant0122122=+=+µµvdvdxdxdtdvdxkxdvdtkx.Then akx=−, akx. This is the condition for simple harmonic motion, that theacceleration of the equivalent particle be a negative constant times the excursion fromequilibrium. By identification with axω2, π==kf2and fk=12πµ.P41.38(a)With x=0 and px=0, the average value of x2is ∆xaf2and the average value of px2is∆px2. Then ∆∆xpx≥=2
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .