Basic quantum mechanics by J. M. Cassels FRS (auth.)

By J. M. Cassels FRS (auth.)

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Both regions are oscillatory, but the wave function discussed in the text is not shown because it is complex, the PCD being non-zero. of a situation where a very large force to the left acts on the particles over a very small interval of x near x = 0. m) \A\ 2 to the right and (hk/m) \B\ 2 to the left, and likewise tClearly an eigenfunction of parity with an even (odd) number of nodes must belong to even (odd) parity. 4)) will usually be taken for granted.

That involves a straightforward but unfortunately lengthy calculation. 26) The same result is predicted by the correspondence principle. An uncertainty ~p in momentum produces an uncertainty in position (~p)t/m after timet: the usual square law has to be used to combine this with the original uncertainty (~x )0 . The product (~x )t ~p, which at t = 0 had the minimum value allowed by the uncertainty principle, increases without limit as time goes on. 5. 2)) plays a central role when fi does not mention t.

And on the right-hand side this is expressed in the neat notation invented by Dirac. 12) The extension to the Dirac notation in the second line here has a symmetrical form which reflects the fact that r may equally well operate on t{12 or t{11. Obviously this notation would be meaningless and inappropriate if the operator concerned were not Hermitian. In future (o/11 lt/Jz) will be called the matrix element of taken between t{i2 and t/J1· An operator which is not Hermitian, k say, also has a matrix element taken between t{12 and t/Jt.

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