Advanced Quantum Mechanics: verschil tussen versies
| Regel 23: | Regel 23: | ||
#* ... | #* ... | ||
#Problem 2: ... | #Problem 2: ... | ||
#* Show how you go from the first formula on page 42 of the lecture notes to the second one. | |||
#Problem 3: Calculations | #Problem 3: Calculations | ||
#* Consider a system composed out of three particles described by the state <math> \alpha|0\rangle|0\rangle|0\rangle+\beta|0\rangle|1\rangle|0\rangle+\gamma|1\rangle|1\rangle|1\rangle </math> in the Hilbert space <math> \mathcal{H}_{1} \otimes \mathcal{H}_{2} \otimes \mathcal{H}_{3} </math>, where <math>\mathcal{H}_{i}=\mathbb{C}^{2} </math> with basis <math> \{|0\rangle,|1\rangle\} </math> and <math> |\alpha|^{2}+|\beta|^{2}+|\gamma|^{2}=1. </math> | #* Consider a system composed out of three particles described by the state <math> \alpha|0\rangle|0\rangle|0\rangle+\beta|0\rangle|1\rangle|0\rangle+\gamma|1\rangle|1\rangle|1\rangle </math> in the Hilbert space <math> \mathcal{H}_{1} \otimes \mathcal{H}_{2} \otimes \mathcal{H}_{3} </math>, where <math>\mathcal{H}_{i}=\mathbb{C}^{2} </math> with basis <math> \{|0\rangle,|1\rangle\} </math> and <math> |\alpha|^{2}+|\beta|^{2}+|\gamma|^{2}=1. </math> | ||
Versie van 20 jan 2021 18:05
About the course
The course is taught by Christian Maes. He tends to be a bit vague, however still informing. The topics are material that were mostly covered in the bachelor, nevertheless you will notice that it is needed. Among the new topics are density matrices, decoherence scattering, quantum optics, a bit of quantum information theory and foundational issues. In November there is a test which does not count for the exam.
Academic year 2020-2021
Maes did go over some things he could ask. Here is a summary.
November test
Solutions of test 4 November 2020
20 January
- Problem 1: True or False
- Every quantum algorithm can be written with classical bits
- Bell showed that there cannot exist a hidden variable.
- The Rabi ... has constant amplitude. (The point was in Rabi model it was true, but in james-cummings not.)
- ...
- ...
- ...
- Problem 2: ...
- Show how you go from the first formula on page 42 of the lecture notes to the second one.
- Problem 3: Calculations
- Consider a system composed out of three particles described by the state in the Hilbert space , where with basis and
- Calculate .
- variational principle to approximate ground state
- Problem 4: Differential cross section of bosons and fermions
- Difference with classical scattering, difference between bosons and fermions (look at 90 degrees), make a sketch of the scattering cross section.
- Problem 5: Time dependent perturbation
Something similar as the following.
- Problem 6: Fun
- How would you solve the measurement problem?
- What are the names of the writers of the EPR paper?
Academic year 2019-2020
Exam 2020 English translation:
1) Oral: A. discuss about symmetries of the Schrödinger equation: when is ? What is rotation invariance? B. mixed states vs superposition of qubits: difference, give example of density matrix, give example of entangled state, calculate its density matrix, is the light in this room a mixture? C. scattering of identical bosons/fermions: difference with classical scattering, difference between bosons and fermions (look at 90 degrees), make a sketch of the scattering cross section.
2) The quantum circuit of the Toffoli gate. What does this gate do?
3) Subaddiditivity: prove that the photon number of coherent states is Poisson distributed.
4) A. Show how you go from the first formula on page 42 of the lecture notes to the second one. (Rewrite the Hamiltonian using an identity of Pauli matrices, and in terms of the magnetic field). B. Calculate .
Academic year 2016-2017
Academic year 2015-2016
Other
You can always look at the old course Advanced topics in QM.