The h Bar

7:14 PM

Hello guys , I tried to read Feynman lectures on electromagnetism, but couldn't really understand it from where the vector fields and gradients and stuff like that . I am also keen on learning quantum mechanics . Well can anyone help me with the pre-requisites needed to understand the Feynman lectures. Or maybe other book recommendations .

I just passed my 12th grade . Thinking of pursuing physics as UG .

John Doe

Hi all

What is the difference between quantum coherent state and a pure state. In this post it seems to imply that they are the same thing?

Anonymous

@Amlanmihir Learning multi-variable calculus and linear algebra would be the first logical step I suppose :)

Amlan mihir

@Blue can you suggest some books for the same ?

Anonymous

@JohnDoe Did you check out the respective Wikipedia pages? It's explained very clearly there

Amlan mihir

they taught calculus in the linear variable at school

Anonymous

7:23 PM

@Amlanmihir Maybe start with Khan Academy

Amlan mihir

@Blue Thank you for helping

Semiclassical

@Blue no idea, I haven't touched the CDF player

John Doe

@Blue The general coherence is explained well, the quantum coherence has a brief explanation which doesn't really draw a distinction between pure states and coherent states.

Semiclassical

the usual distinction is between pure states and mixed states

coherent states are a bit more specific

Anonymous

Coherent states

In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. The quantum harmonic oscillator and hence, the coherent states, arise in the quantum theory of a wide range of physical systems. For instance, a coherent...

Semiclassical

7:26 PM

you talk about pure states when doing the density matrix formalism.

John Doe

@Blue Yeah I read it, it seems to imply that pure states and coherent states are the same thing. Is that correct?

Semiclassical

no.

a pure state can be described by a single wavefunction $|\psi \rangle$

A coherent state is a specific instance of such a pure state, namely one which has minimal uncertainty product

in the density matrix formalism, a pure state would be written as $\rho=|\psi\rangle\langle \psi|$

whereas a mixed state would be a linear combination of such i.e. $\rho=\sum_k|p_j \psi_j \rangle \langle \psi_j|$

So coherent states are special cases of pure states, and pure states are special cases of mixed states.

John Doe

@Semiclassical Okay thanks. What would be an example of a pure state which is not a coherent state?

Semiclassical

A particle in the ground state of a box is an obvious one.

If you measure the energy, you'll always get the same value. But if you work out the uncertainty product for it, then it's always larger than $\hbar/2$.

most examples of wavefunctions you see in textbooks will not be coherent, really

the main exception being the ground state of a harmonic oscillator

that one has $\Delta x \Delta p=\hbar/2$ and so is a coherent state

But the excited states of the harmonic oscillator aren't coherent

So being a coherent state is a very special case.

John Doe

7:43 PM

@Semiclassical Could you give an example of a two dimensional quantum system wuch as in this post which is a pure state but not a coherent state?

In that post he gave example of a pure state which is a coherent state.

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