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V(x) = 00, V(x) = 0, x< 0, x 2 a 0 < x < a %3D a x The eigenfunction, labeled by the quantum number n, are. ппх Pn = A sin a The energy eigenvalues is n?n²h? E 2mа? a) Find A (Show your work) b) Find the probability density that this electron will be found between 0 and n c) For any state n, Find the expectation value of the position of the electron. d) If the electron goes from n 5 to n 3 level finds the width of the box if the frequency of the emitted photon is v. (your answer should be written in terms

V(x) = 00, V(x) = 0, x< 0, x 2 a 0 < x < a %3D a x The eigenfunction, labeled by the quantum number n, are. ппх Pn = A sin a The energy eigenvalues is n?n²h? E 2mа? a) Find A (Show your work) b) Find the probability density that this electron will be found between 0 and n c) For any state n, Find the expectation value of the position of the electron. d) If the electron goes from n 5 to n 3 level finds the width of the box if the frequency of the emitted photon is v. (your answer should be written in terms

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An electron of mass m is confined to an infinitely deep square well potential. V(x) = 00, V (x) = 0, x< 0, x 2 a 0 < x < a a The eigenfunction, labeled by the quantum number n, are. ппх Pn = A sin a The energy eigenvalues is n'n?h? E = 2mа? a) Find A (Show your work) а b) Find the probability density that this electron will be found between 0 and c) For any state n, Find the expectation value of the position of the electron. d) If the electron goes from n = 5 to n 3 level finds the width of the box if the frequency of the emitted photon is v. (your answer should be written in terms of v and h (not including h )) e) If the electron is in the third excited state compute the force that the electron exerts on the wall during an impact on either wall. (your answer should be written in terms of a.) f) If the electron now confined inside a cubic box with edge of length a. Show that 1472h2 there are six different wave functions that have E = 2ma?
Transcribed Image Text:An electron of mass m is confined to an infinitely deep square well potential. V(x) = 00, V (x) = 0, x< 0, x 2 a 0 < x < a a The eigenfunction, labeled by the quantum number n, are. ппх Pn = A sin a The energy eigenvalues is n'n?h? E = 2mа? a) Find A (Show your work) а b) Find the probability density that this electron will be found between 0 and c) For any state n, Find the expectation value of the position of the electron. d) If the electron goes from n = 5 to n 3 level finds the width of the box if the frequency of the emitted photon is v. (your answer should be written in terms of v and h (not including h )) e) If the electron is in the third excited state compute the force that the electron exerts on the wall during an impact on either wall. (your answer should be written in terms of a.) f) If the electron now confined inside a cubic box with edge of length a. Show that 1472h2 there are six different wave functions that have E = 2ma?
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