2. Theoretische Physik III Quantenmechanik M. Sekania A. P. Kampf Animated Quantum Mechanics Outlook: Time Development of Gaussian Wave Packet Time Development of Gaussian Wave Packet Time Dependent Harmonic Oscillator Time Dependent Harmonic Oscillator Time Dependent Anharmonic Oscillator Time Dependent Anharmonic Oscillator Some useful links and literature Some useful links and literature All animations were obtained from the following web pages: http://webphysics.davidson.edu/Applets/QTime/QTime_Examples.html http://rugth30.phys.rug.nl/quantummechanics/

3. Theoretische Physik III Quantenmechanik M. Sekania A. P. Kampf Initial wavefunction: (Gausian wave packet) Initial wavefunction: e i(2 x) e -(x+15)² (Gausian wave packet) Time Development of Gaussian Wave Packet Initial wavefunction: e -x² (Gausian wave packet)

4. Theoretische Physik III Quantenmechanik M. Sekania A. P. Kampf Initial wavefunction: What will hapen if you reverse the time continue expanding ?continue expanding ? contract forever ?contract forever ? contract to its initial width and expand again ?contract to its initial width and expand again ? remain the same?remain the same?

5. Theoretische Physik III Quantenmechanik M. Sekania A. P. Kampf Time Dependent Harmonic Oscillator Potential: x 2 (harmonic potential) Initial wavefunction: e -x² (Gausian wave packet) Potential: x 2 (harmonic potential) Initial wavefunction: e -ax² (Gausian wave packet) For which a the form of the wave packet does not change?

6. Theoretische Physik III Quantenmechanik M. Sekania A. P. Kampf Potential: x 2 Initial wavefunction: e -(x+6)² Is it possible to prepare such a wave packet for which the form of the wavefunction will not change?

7. Theoretische Physik III Quantenmechanik M. Sekania A. P. Kampf Time Dependent Anharmonic Oscillator Potential: x 4 Initial wavefunction: e -x² (Gausian wave packet) Potential: x 4 Initial wavefunction: e -(x+6)² (Gausian wave packet)

8. Theoretische Physik III Quantenmechanik M. Sekania A. P. Kampf Some useful links and literature http://webphysics.davidson.edu/Applets/QTime/QTime_Examples.html http://webphysics.davidson.edu/Applets/QTime/QTime_Examples.htmlhttp://webphysics.davidson.edu/Applets/QTime/QTime_Examples.html http://rugth30.phys.rug.nl/quantummechanics/ http://rugth30.phys.rug.nl/quantummechanics/http://rugth30.phys.rug.nl/quantummechanics/ Iteractive Quantum Mechanics Iteractive Quantum Mechanics Siegmund Brandt, Hans Dieter Dahmen, Tilo Stroh (Springer) Siegmund Brandt, Hans Dieter Dahmen, Tilo Stroh (Springer) The Picture Book of Quantum Mechanics The Picture Book of Quantum Mechanics Siegmund Brandt, Hans Dieter Dahmen (Springer) Siegmund Brandt, Hans Dieter Dahmen (Springer)