3k views

### What do imaginary numbers practically represent in the Schrödinger equation? [duplicate]

I know that the $i$ that appears in the Schrödinger equation, which is the imaginary unit, is used to solve problems that arise with roots of negative numbers. But what is the meaning of that negative ...
3k views

### Why is the wave function complex? [duplicate]

Why should an equation (TDSE) in which first time derivative is related to second space derivative have a solution that contains $i$?The wave function is supposed to be complex, but I am unable to ...
214 views

### Why is $i$ used in the equations for quantum mechanics? [duplicate]

Coming from someone who knows a tiny bit about the subject but who really wants to learn. I know it's the square root of -1 but I would like some insight as to why it's used at all.
431 views

### Why is it necessary to use the imaginary number in QM? [duplicate]

My professor argues that one of the fundamentally unique properties of Quantum Mechanics is that the imaginary unit i is not removable (you can't avoid using it, unlike in other areas of physics like ...
91 views

### Could the phase factor $i$ be replaced by “matrix representation” totally in quantum mechanics? [duplicate]

It seems that $i$ plays an important role in quantum mechanics (Q.M.). On the other hand, linear algebra plays such an important role in Q.M. too. So would linear algebra, such as a matrix be able to ...
83 views

### Why is a quantum state described by a complex vector in the Hilbert space? [duplicate]

In classical theory (e.g., classical mechanics and electromagnetic theory), we introduce the complex values for the mathematical convenience, e.g., A=(a+a*)/2. There, the use of complex values (or ...
80 views

### Is there a way to explain quantum mechanics without invoking complex numbers? [duplicate]

"Every possible history starting from a particular state and ending at a particular state is assigned a complex number by some predefined rules in particular that the complex number is the product of ...
66 views

### What is Wave Function? [duplicate]

Well, what is the meaning of wave function? What does it represent? In Schrodinger's equation, we find the value of Ψ. But what is Ψ exactly? Max Born only gave an explanation of what $Ψ^2$ (the ...
42 views

### Imaginary part of the waveefunction in quantum mechanics [duplicate]

I wonder what is the reason for wave function in quantum mechanics to have an imaginary part... How do we interpret the utility of the imaginary part?! As we know the wave function it self does not ...
19k views

### QM without complex numbers

I am trying to understand how complex numbers made their way into QM. Can we have a theory of the same physics without complex numbers? If so, is the theory using complex numbers easier?
4k views

### Why are Only Real Things Measurable?

Why can't we measure imaginary numbers? I mean, we can take the projection of a complex wave to be the "viewable" part, so why are imaginary numbers given this immeasurable descriptor? Namely with ...
3k views

### Can one do the maths of physics without using $\sqrt{-1}$?

The use of imaginary and complex values comes up in many physics and engineering derivations. I have a question about that: Is the use of complex numbers simply to make the process of derivation ...
2k views

### Why is the contribution of a path in Feynmans path integral formalism $\sim e^{(i/\hbar)S[x(t)]}$

In Feynman's book "Quantum Mechanics and Path Integrals" Feynman states that the probability $P(b,a)$ to go from point $x_a$ at time $t_a$ to the point $x_b$ at the time $t_b$ is \$P(b,a) = \|K(b,a)...