Does anyone know any nice examples of vector spaces without a basis that is in some sense "natural". To clarify what I mean, suppose we look at $\mathbb{R}^2$. We define $\mathbb{R}^2$ as pairs of real numbers. In some sense, what we are doing is expressing vectors in terms of a natural basis : ...

I have seen websites and videos that show how cancer cells can be destroyed using sound resonance oscillation. So has anyone heard of anyone who is in the field of sound resonance trying to capture the wavelength of the Corona virus so we can create a Sonogram machine to use against this virus pa...

It's a nice idea. Sadly it won't work but there is still some interesting physics involved. As a general rule resonance is only an efficient way to transfer energy to an object if that object has a high Q factor. A high Q factor means the energy supplied builds up and increases the amplitude of ...

I often see that the density operator in $1^{st}$ quantization is defined to be: $$ \hat n(\vec r)=\sum_{i=1}^N \delta(r-\hat r_i)$$ In canonical quantization it is given by $$ \hat n(\vec r)=\hat \psi^\dagger(\vec r)\hat\psi(\vec r)$$ but shouldn't there be a factor of $N$ multiplying since in ...

So I was reading some papers, mainly in the Green's functions theory of the time-independent Schroedinger equation, and came across an equation that had a term similar to: $$\frac{\partial \Psi_n^*(x)\Psi_n(x')}{\partial E_n}$$ Basicially asking to evaluate the derivative of an energy eigenstat...