Hello all. I am new here. I am in the last quarter of a 3 quarter sequence of undergrad quantum mechanics and I just had some conceptual questions (nothing pertaining to homework). We just recently covered Berry's Phase and the Dynamical Phase. Now I wanted to start with a more basic quantum mechanical question before moving to Berry's Phase:(adsbygoogle = window.adsbygoogle || []).push({});

When determining a wavefunction $$\psi$$ we can pretty much derive a wavefunction "up to" a phase, i.e $$\psi = A \left(functions\right) e^{i \chi}$$ Now, if I am understanding elementary group theory correctly, a U(1) transformation would be multiplying our initial function by a complex exponential with a phase. So, is the wavefunction I wrote "up to a phase" basically transformed by U(1)?

Okay, assuming what I first asked is legitimate, I wanted to ask about Berry and Dynamical Phases. Through the adiabatic approximation we can write $$\Psi_n\left(t\right) = \psi_n \left(t \right) e^{i \theta_n \left(t \right)} e^{i \gamma_n \left(t \right)} $$. My question here is if any of this may be similar or is a U(1) transformation, or is it not so because of the possible time dependence?

Relevant equations:

$$\theta_n \left(t \right) =-\frac{1}{\hbar} \int_{0}^{t} E_n\left(t'\right) dt'$$

$$\gamma_{n} \left(t \right) = i \int_{0}^{t} \langle \psi_m\left(t'\right) | \frac{\partial}{\partial t'} \psi_{m}\left(t' \right) \rangle dt'$$

Thank you all for your patience and help!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quantum Mechanics and Group Theory questions

Loading...

Similar Threads - Quantum Mechanics Group | Date |
---|---|

A Is non-linear quantum mechanics (even) plausible? | Yesterday at 8:16 PM |

A Can disjoint states be relevant for the same quantum system? | Tuesday at 3:58 PM |

Good books on the group theory of quantum mechanics | Jan 13, 2015 |

Group theory and quantum mechanics | Apr 8, 2014 |

Generalized group for quantum mechanics | Apr 22, 2011 |

**Physics Forums - The Fusion of Science and Community**