# Index [[Avoided crossing]] [[Bloch's theorem]] [Bloch vector](Bloch%20vector) [[Degenerate Energy levels]] [[Energy of a quantum system (time independent)]] [Energy of a two-level system (time independent)](Energy%20of%20a%20two-level%20system%20(time%20independent).md) [Hamiltonian operator (time independent)](Hamiltonian%20operator%20(time%20independent)) [Ladder operators](Ladder%20operators.md) [[momentum eigenstate]] [Momentum Operator](Momentum%20Operator.md) [Pauli Matrices](Pauli%20Matrices.md) [[Periodic potentials]] [Phase space distributions (quantum mechanics)](Phase%20space%20distributions%20(quantum%20mechanics).md) [[position eigenstate]] [Position Operator](Position%20Operator.md) [Potential Barrier](Potential%20Barrier.md) [[Quantum superposition]] [[Schrödinger equation (time independent)]] [[Stationary two-level systems]] [[Time-independent quantum perturbation theory]] # Sub-Indices [Quantized Angular momentum (index)](Quantized%20Angular%20momentum%20(index).md) [Quantum Harmonic Oscillator (index)](Quantum%20Harmonic%20Oscillator%20(index).md) --- # Proofs [Proof of Bloch's theorem in terms of translation operations](Proof%20of%20Bloch's%20theorem%20in%20terms%20of%20translation%20operations.md) --- # Basic concepts The section dubbed [stationary quantum systems](Stationary%20Quantum%20Systems%20(Index).md) should be taken as quantum mechanics in terms of freeze frames - a picture of quantum physics that treats every system as unchanging. We also treat quantum systems as either non-interacting or under some external potential whose source we don't model. ^afe0e2 Thus, here we only include topics that may be adequately described in terms of single [state vectors](State%20vector.md) or [wave functions](Wavefunction.md). In many elementary examples, this describes single particles, however, there are quantum systems that may be composed of a few or many particles but are still adequately described by single state vectors (see [coherent states,](coherent%20state.md) for example). Thus the basis of this section is anything pertaining to the [first and second postulate in quantum mechanics,](Postulates%20of%20Quantum%20Mechanics.md) where we define the notion of state vectors followed by [observables,](Observable.md) which we use to build quantum mechanical models that explain the properties of state vectors. ## Debroiglie wavelengths The _Debroiglie wavelength_ is a property of all [quantum systems](Quantum%20systems.md) that is relevant also when considering [stationary quantum systems](Stationary%20Quantum%20Systems%20(Index).md) (i.e., quantum systems in terms of [freeze frames.](stationary%20quantum%20systems%20(index)#^afe0e2)) #^39bbae) --- # Bibliography [Ashcroft N. W., Mermin, N. D.,_Solid State Physics_, Harcourt College Publishers, 1976.](Ashcroft%20N.%20W.,%20Mermin,%20N.%20D.,%20Solid%20State%20Physics,%20Harcourt%20College%20Publishers,%201976..md) Commins, E.D. _Quantum Mechanics: And Experimentalist Approach_ .pdf) Dirac, P. A. M., _The Principles of Quantum Mechanics_, Oxford Univ Press, Revised 4th edition (1978) %20-%20libgen.lc.pdf) Mukhanov V., Homework 10, Quantum Mechanics 2 (2019/2020)   [Baym, G., _Lectures on Quantum Mechanics_, Westview Press, 1990](Baym,%20G.,%20Lectures%20on%20Quantum%20Mechanics,%20Westview%20Press,%201990.md) [Franklin, J., Harmonic Oscillator Physics, Lecture 9, Physics 342, _Quantum Mechanics I_, Lecture Notes, Spring 2010](Franklin,%20J.,%20Harmonic%20Oscillator%20Physics,%20Lecture%209,%20Physics%20342,%20Quantum%20Mechanics%201,%20Lecture%20Notes,%20Spring%202010.md) [Kittel, C., _Introduction to Solid State Physics_, Wiley & Sons, 8th edition, 2005](Kittel,%20C.,%20Introduction%20to%20Solid%20State%20Physics,%20Wiley%20&%20Sons,%208th%20edition,%202005..md) [Likharev, K., _Essential Graduate Physics-Quantum Mechanics_, LibreTexts, 2024](Likharev,%20K.,%20Essential%20Graduate%20Physics-Quantum%20Mechanics,%20LibreTexts,%202024.md) [Mandel L., Wolf E., _Optical Coherence and Quantum Optics_, Cambridge University Press, 1995.](Mandel%20L.,%20Wolf%20E.,%20Optical%20Coherence%20and%20Quantum%20Optics,%20Cambridge%20University%20Press,%201995..md) [McGreevy, John. A., Physics 212A Lecture Notes, Fall 2015.](McGreevy,%20John.%20A.,%20Physics%20212A%20Lecture%20Notes,%20Fall%202015..md) [Sakurai, J. J., Napolitano J., _Modern Quantum Mechanics_, Addison-Wesley, 2nd Edition, 2011](Sakurai,%20J.%20J.,%20Napolitano%20J.,%20Modern%20Quantum%20Mechanics,%20Addison-Wesley,%202nd%20Edition,%202011.md) [Shankar, R., _Principles of Quantum Mechanics_, Plenum Press, 2nd edition, 1994.](Shankar,%20R.,%20Principles%20of%20Quantum%20Mechanics,%20Plenum%20Press,%202nd%20edition,%201994..md) [Schollwöck, U. _Grundlegende Formulismus 1-2_, T2, Quantenmechanik, Lecture Notes, Winter 2019-2020.](Schollwöck,%20U.%20Grundlegende%20Formulismus%201-2,%20T2,%20Quantenmechanik,%20Lecture%20Notes,%20Winter%202019-2020..md) [Schollwöck, U. Homework 0, _Quantum Mechanics 1_ (German) (2019-2020)](Schollwöck,%20U.%20Homework%200,%20Quantum%20Mechanics%201%20(German)%20(2019-2020).md) #QuantumMechanics/StationaryStateQuantumSystems #QuantumMechanics/StationaryStateQuantumSystems/QuantizedAngularMomentum #QuantumMechanics/StationaryStateQuantumSystems/QuantumHarmonicOscillators #QuantumMechanics/ApproximationMethods/QuantumPerturbationTheory #index #Bibliography