# Tag Info

Accepted

### Contradiction in my understanding of wavefunction in finite potential well

Even classically, particles with a fixed total energy spend more time near the turning points since this is where the motion is the slowest. The probably of finding the particle in a small region ...

### Contradiction in my understanding of wavefunction in finite potential well

Imagine a perfectly elastic ball dropped vertically onto a flat surface. The ball heads for the point of lowest potential, ie the ground, but because of conservation of energy it bounces back to its ...
Accepted

### The reasoning of the definition of $S$-matrix

As lurscher already said correctly, the idea is to choose an initial and a final time that is (in time) away from the actual time-dependent interaction in order to make sure that the interaction does ...
Accepted

### Wrong formuation of Heisenberg uncertainty principle

Don't be confused it is definitely $$\Delta E \Delta t \geq \frac{\hbar}{2}$$ Your professor typo'd here, as if what he wrote then we could measure energy with any arbitrarily small error we want ...

1 vote
Accepted

### Deriving a recursion relation for Clebsch-Gordan coefficients

Where you went wrong is comparing apples and oranges. Your superb text is right. By the time it utilized (3.369), it "translated" the unconventional (3.370) into the standard convention, (3....
1 vote
Accepted

### Can the expectation value behave like a function?

Consider a harmonic oscillator with mass $m$ and frequency $\omega$, and the state : $$|\psi\rangle = \frac 1{\sqrt{2}}\left(|0\rangle + i|1\rangle\right)$$ In this state we have : \begin{align} \...
1 vote

In condensed matter many-body physics vacuum usually means a state filled up to the Fermi energy (such as the ground state of conduction band in a metal), i.e., $$a_\mathbf{p}|0\rangle = 0 \text{ if ... 1 vote Accepted ### Pure state vs mixed state in this example Yes your reasoning is entirely correct. You would now describe the state at hand with the density operator$$ \rho = |c_1|^2 |\psi_1 \rangle \langle \psi_1| + |c_2|^2 |\psi_2 \rangle \langle \psi_2|$$... 1 vote Accepted ### Question regarding exercise of dynamics of spin-1/2 system You need to do everything explicitly in the basis \{|+\rangle,|-\rangle\}. So you have$$|\psi(t)\rangle=\begin{pmatrix} \psi_+(t) \\ \psi_-(t) \end{pmatrix} \quad\text{and}\quad |\tilde{\psi}(t)\...

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