Recent content by jahlex

Homework Statement Given that A is a square matrix and A^\dagger is its Hermitian conjugate, and that A^\dagger A = 0, show that A = 0. The Attempt at a Solution Let \{|i\rangle\} be some orthonormal basis. Find the matrix elements of A by taking 0 = \langle j| A^\dagger A |j \rangle =...

Hello, The attached file gives survey statistics on the most used textbooks for core graduate physics courses (on the bottom of pages 3-7). For example, the data show that 76 out of 80 surveyed American physics departments use Jackson's book for their Electromagnetism course. I'm wondering...

Homework Statement Let G be a finite complex matrix group: G \subset M_{n\times n}. Show that, for g \in G, |\text{tr}(g)| \le n and |\text{tr}(g)| = n only for g = e^{i\theta}I. 2. The attempt at a solution Since G is finite, then every element g \in G has a finite order: g^r = I for some...

The problem: Killer Asteroid Some data: Mass of Earth = 6.0 x 1024 kg Radius of Earth = 6.4 x 10³ km Gravitational constant G = 6.67 x 10−11N-m/kg² You receive an urgent phone call from NASA. Their scientists have just detected an asteroid headed for Earth. Its mass is 6 x 10 15 kg, which is...