LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

... Part – C (4 x 12.5 = 50 Marks ) (Answer any four questions) 16. Obtain Newton’s second law of motion from Ehrenfest’s theorem. 17. Find the transmission coefficient of a particle moving along the x-axis encountering a potential barrier of breadth ‘a’ and height V0, if the energy of the particle E < ...

... Part – C (4 x 12.5 = 50 Marks ) (Answer any four questions) 16. Obtain Newton’s second law of motion from Ehrenfest’s theorem. 17. Find the transmission coefficient of a particle moving along the x-axis encountering a potential barrier of breadth ‘a’ and height V0, if the energy of the particle E < ...

763313A QUANTUM MECHANICS II Exercise 1 1. Let A and B be

... 3. Calculate the expectation values hα|σi |αi, i = 1, 2, for Pauli spin matrices σ1 and σ2 with respect to an arbitrary state |αi = α1 |1i + α2 |2i. Here |1i and |2i are the eigenvectors of σ3 . 4. Consider a three-dimensional vector space spanned by an orthonormal basis |1i, |2i, |3i. Kets |αi and ...

... 3. Calculate the expectation values hα|σi |αi, i = 1, 2, for Pauli spin matrices σ1 and σ2 with respect to an arbitrary state |αi = α1 |1i + α2 |2i. Here |1i and |2i are the eigenvectors of σ3 . 4. Consider a three-dimensional vector space spanned by an orthonormal basis |1i, |2i, |3i. Kets |αi and ...

3.1 Linear Algebra Vector spaces

... hα | T̂ | βi = hα | iihi | T̂ | jihj | βi = αi∗Tij βj = (αiTij ∗)∗βj = (αi{T†}ji)∗βj = ({T†}jiαi)∗βj i.e., T̂ † is that transformation which, when applied to the first member of an inner product, gives the same result as if T̂ itself had been applied to the second vector. Four properties: 1. any Her ...

... hα | T̂ | βi = hα | iihi | T̂ | jihj | βi = αi∗Tij βj = (αiTij ∗)∗βj = (αi{T†}ji)∗βj = ({T†}jiαi)∗βj i.e., T̂ † is that transformation which, when applied to the first member of an inner product, gives the same result as if T̂ itself had been applied to the second vector. Four properties: 1. any Her ...

Homework Set 3

... the form of the whole series (leading to sines and cosines); that is, you are not required to do a rigorous demonstration by mathematical induction. As for part 2, you should make explicit use of part 1! Note that the series terminates after the ...

... the form of the whole series (leading to sines and cosines); that is, you are not required to do a rigorous demonstration by mathematical induction. As for part 2, you should make explicit use of part 1! Note that the series terminates after the ...