Physics

Which of the following describe the expansion coefficients for a general state? $a_{n}=\langle \psi _{n}\vert \psi \rangle =\int _{-\infty }^{\infty }dx\psi _{n}^{\ast }(x)\psi (x)$ $a_{n}=(\sum _{n}\vert \psi _{n}\rangle )\vert \psi \rangle $ $a_{n}=\langle \psi _{n}\vert \psi \rangle ^{\ast }=\int _{-\infty }^{\infty }dx\psi _{n}(x)\psi ^{\ast }(x)$ $a_{n}=\langle \psi _{n}\vert \psi _{m}\rangle =\int _{-\infty }^{\infty }dx\psi _{n}^{\ast }(x)\psi _{m}(x)$

A certain wave function is given by $\psi (x)=\{ \begin{matrix} A&for-a\leqslant x\leqslant a\\ 0&otherwise\end{matrix} $ Which of the following corresponds to the Fourier transform for this wave function? A sum of spherical harmonics. A sum of sines and cosines. A sum of Hankel functions. The Dirac delta function.

8> What is the random capture theory? Which theory best explains how our solar system was created?

A wave function can be expanded in basis states as $\vert \psi \rangle =\sum _{n}a_{n}\vert \psi _{n}\rangle $ What must be true of the expansion coefficients? $\sum _{n}\vert a_{n}\vert ^{2}=1$ They must be real numbers. There is no restrictions on the coefficients. $\sum _{n}a_{n}=1$

Match each statement to the wave interaction it describes. \begin{array}{|l|l|} \hline\ reflection\ &\ Waves\ bounce\ off\ an\ object.\ \\ \hline\ absorption\ &\ Waves\ are\ taken\ in\ by\ an\ object.\ \\ \hline\ transmission\ &\ Waves\ bend\ while\ passing\ from\ one\ medium\ to\ another.\ \\ \hline\ diffraction\ &\ Waves\ scatter\ through\ an\ opening\ or\ around\ an\ object.\ \\ \hline\ retraction\ &\ Waves\ go\ through\ an\ object.\ \\ \hline \end{array}

Which of the following expressions correspond to the energy-time uncertainty principle? $\Delta E\Delta t\geqslant 2\bar {h}$ $\Delta E\Delta t\geqslant \hat {h}$ $\Delta E\Delta t\geqslant \frac {h}{2}$ $\Delta \omega \Delta t\geqslant \bar {h}$

Consider the following force: A fridge magnet is pulling on a paper clip. According to Newton's third law what other force must be happening? The paper clip is pushing on the fridge magnet. The paper clip is pulling on the fridge magnet.

Which of the following correspond to the first-order shift in energies using time-independent perturbation theory? $\vert \langle \psi _{n}^{0}\vert \delta \hat {H}\vert \psi _{n}^{0}\rangle \vert ^{2}$ $\langle \psi _{n}^{0}\vert \delta \hat {H}\vert \psi _{n}^{0}\rangle $ $\sum _{m\neq n}\frac {\langle \psi _{n}^{0}\vert \delta \hat {H}\vert \psi _{n}^{0}\rangle }{E_{m}^{0}-E_$ $\sum _{m\neq n}\frac {\vert \langle \psi _{m}^{o}\vert \delta \hat {H}\vert \psi _{n}^{o})\vert ^{2}}{E_{m}^$

Which one of the following actions will increase the current ratio, all else constant? Assume the current ratio is greater than 1.0

If a wave function is given in terms of orthonormal wave functions as $\vert \psi \rangle =\frac {1}{\sqrt {5}}\vert \psi _{1}\rangle +\sqrt {\frac {3}{5}}\vert \psi _{2}\rangle +A\vert \psi _{3}\rangle $ Then what must be true about A? $\frac {1}{\sqrt {5}}$ $\frac {1}{2}$ There is not enough information to determine A. $\frac {1}{5}$