(a)
Interpretation:
The identity
Concept introduction:
The integral of a wave function and the conjugate of another wavefunction over a restricted region represent the orthogonality of both the wave functions. If the integral is zero, the wavefunctions are orthogonal to each other. Trigonometric identities are used to simplify the integrals.
(b)
Interpretation:
Considering the case
Concept introduction:
The cosine graph is a periodic graph. It is an even function. The area under the curve above the x axis is equal to the area under the curve below the x axis.
(c)
Interpretation:
The area enclosed between the curves and x axis is zero and hence the integral is zero has to be shown in both cases.
Concept introduction:
The area under the curve of a wavefunction is equal to the value of integral for that function. The integral of a wave function and the conjugate of another wavefunction over a restricted region represent the orthogonality of both the wave functions. If the integral is zero the wavefunctions are orthogonal to each other.
(d)
Interpretation:
The argument in (c) has to be generalized for the case of arbitrary
Concept introduction:
The integral of a wave function and the conjugate of another wavefunction over a restricted region represent the orthogonality of both the wave functions. If the integral is zero the wavefunctions are orthogonal to each other..
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Atkins' Physical Chemistry
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