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Demonstrate that the wave functions of the stationary states of a particle confined in a unidimensional potential well with infinitely high walls are orthogonal i.e., theysatisfy the conditions int_(0)^(l)psi_(n)psi_(n),dx=0 if n'!=n. Herel is thewidth of the well ,n are integers. |
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Answer» SOLUTION :The WAVE function is given in 6.77. we see that `int_(0)^(L)Psi_(n)(x)Psi_(n)(x)d(x)-(2)/(l)int_(0)^(1)`sin`(n pix)/(l)`sin`(n'pi x)/(l)dx` `=(1)/(l)int_(0)^(l)[cos(n-n')(pix)/(l)-cos(n+n')(pix)/(l)]dx` `=(1)/(l)[sin(n-n')pi x//l)/((n-n')(pi)/(l))-(sin(n+n')(pix)/(l))/((n+n')(pix)/(l))]_(0)^(l)e` If `n=n'`, this is zero as `n` ADN `n'` are integers. |
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