Solve your IGNOU Doubts

Question:

Explain why a polynomial is a useful choice for an interpolating function.

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Question:

The series for e^x can be written as:

$$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots$
Calculate the truncation error when the first four terms of the series are used to evaluate e^1.5.

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Question:

Explain round-off error and truncation error, with one example of each.

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Question:

Using molecular orbital method, construct all pssible trial wavefunctions (including spin) for a diatomic molecule. Of these functions, which trial function is expected to have the minimum energy? Give justification for your answer.

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Question:

Using Thomas-Fermi method, derive an expression for the total kinetic energy of N electrons in a cubic box of side L, and hence obtain the expression for pressure.

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Question:

The anti-symmetric spin function for a two electron system is given as:
$$\chi_-(1, 2) = \frac{1}{\sqrt{2}}[\alpha(1)\beta(2) - \beta(1)\alpha(2)]$ $
Prove that $\chi_-(1, 2)$ is an eigenfunction of $(\hat{S})^2$ .

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Question:

Consider K meson of mass m_K decaying into two pions of mass $m_\pi$ each, in the laboratory frame. Show that the energy of each pion is equal to $\frac{m_K}{2}$ and the momenta are $p_\pi = \frac{1}{2}\sqrt{m_K^2 - 4m_\pi^2}$ .

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Question:

a) Determine the shift in energy caused by relativistic correction to kinetic energy for $n=2$ and $n=1$ levels of hydrogen atom. Using appropriate selection rules, show which transitions are allowed.

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Question:

Write down the wave function for $|\pi^-\rangle$ . Use the isospin raising operator to derive the wavefunctions for $|\pi^0\rangle$ and $|\pi^+\rangle$ .