# Tagged Questions

Numbers of the form $\{z= x+ i\,y:\;x,\, y\in\mathbb{R}\}$ where $i^2 = -1$. Useful especially as quantum mechanics, where system states take complex vector values.

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### Module of $SU(2)$ [closed]

I've read that "$SU(2)$ is the group of transformations in 2-dimensional complex space." What specifically are the two complex dimensions? Is one dimension the real axis and the other the ...
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### What is the mathematical motivation for complexifying momenta in BCFW?

One of the first steps in obtaining the on-shell BCFW recursion relations is complexifying the momenta of the external particles. Now complexifying things is not unprecedented (the dispersion program ...
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### What does the Schrodinger Equation really mean?

I understand that the Schrodinger equation is actually a principle that cannot be proven. But can someone give a plausible foundation for it and give it some physical meaning/interpretation. I guess I'...
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### Should the complex conjugate of a derivative of a Grassmann number include a sign?

Take a real Grassmann variable, by which I mean $\theta=\theta^*$. We have $$\int d\theta~ \theta =1,\qquad \frac{\partial}{\partial\theta}\theta=1$$ If I define the conjugation of Grassmann ...
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### Why Does there Have to be Linearity in Ket and Skew Symmetry?

I'm reading Shankar's "Principles of Quantum Mechanics," and on page 8 he states that one axiom in Dirac notation is linearity in ket, and because they are also skew symmetric there is anti-linearity ...
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### Integral over a product of two Green's functions

Need some help here on a frequently encountered integral in Green's function formalism. Forgive me since I am a junior student. I have an integral/summation as a product of a retarded and advanced ...
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### Why does a electric Potential have to be real, but not a Potential in quantum mechanics?

So I had this Problem when I had to learn about classical electromagnetism: Why is it, that we use complex numbers when calculating stuff, but in the end only the real part is important (for example ...
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### Complex conjugate of the Schrödinger equation?

This might be a very simple question but I don't understand how to compute the complex conjugate of the Schrödinger equation: $$i\partial_t \psi = H\psi$$ where $H$ is an hermitian operator. How to ...
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### Is there a way to prove that a bound state wavefunction can always be chosen real for an arbitrary potential in Quantum Mechanics?

As we can prove many things that always (at least in introductory quantum mechanical problems) apply using an arbitrary potential (like that $E>V_{\rm min}$ or else the solutions are non-...
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### What are functions of a complex variable used for in physics?

Whenever someone asks "Why are complex numbers important?" the answer, at least in the context of physics, usually includes things like quantum mechanics, oscillators and AC circuits. This is all very ...
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### Can the quantum mechanical current density be imaginary?

I am dealing with a situation where I get an imaginary transmission current density. Is this possible? Does it imply a zero transmission probability?
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### Significance of $i$ in the Schrödinger equation [duplicate]

There's an imaginary $i$ in the Schrödinger equation, which I guess is to define the position of the particle in a space-time involving a complex function. But what is the real physical significance ...
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### Complex tetrad vs. Real metric

I asked this question almost a month ago on mathoverflow (http://mathoverflow.net/q/228138/) but received no response. I thought I could have better luck here: I have a question on the relationship ...
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### Can a qubit have an imaginary component?

My knowledge of linear algebra is limited and my physics knowledge mostly comes from high school and Youtube so please bear with me. In the equation $$|x\rangle = a|0\rangle+b|1\rangle,$$ I read that ...
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### How can $F_0\cos\omega t$ change to $F_0e^{i\omega t}$ in driven oscillator equation?

I have one thing that confuses me on deriving the solution for the Linear Forced Oscillator. Suppose we have the equation as $$ma + rv + kx = F_0 \cos \omega t$$ What confuses me is when the driving ...
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### The derivation of the irreducible representations of the Lorentz group

I took the way of classification of Lorentz group representations from Sexl, Urbantke, Relativity, groups and particles (Germ. ed. 1975). But I don't understand it as I outline in the following: In ...
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### Non-equivalence between $\omega \to \omega \pm i\varepsilon$ and Cauchy principle value

I am looking to gain a more rigorous and deeper understanding as to how an $i\varepsilon$ prescription actually changes the end result of a divergent integral, specifically in regards to Green's ...
### Eigenvalue problem $−\psi''(x) − (ix)^ N \psi(x) = E\psi(x)$ in complex plane
To find the eigenvalue in the complex plane of $x$ for one dimensional Schrodinger equation $$−ψ''(x) − (ix)^ N ψ(x) = Eψ(x).$$ where $N$ can be any real number, the boundary condition $ψ(x) → 0$ ...
The index of refraction which represents how much light gets refracted when entering a medium is defined as $$n = \frac{c}{v}$$ I have seen it stated in several places, such as here, that we can ...