Linked Questions

2
votes
7answers
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 ...
0
votes
1answer
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 ...
0
votes
2answers
202 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.
2
votes
1answer
406 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 ...
2
votes
0answers
89 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 ...
2
votes
0answers
82 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 ...
0
votes
0answers
79 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 ...
-1
votes
1answer
63 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 ...
1
vote
0answers
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 ...
76
votes
12answers
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?
33
votes
7answers
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 ...
30
votes
7answers
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 ...
28
votes
8answers
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)...
17
votes
6answers
5k views

Disproof of Bell’s Theorem

The half-page arxiv doc by Joy Christian of Oxford Uni, UK has the Title and Abstract: Disproof of Bell’s Theorem We illustrate an explicit counterexample to Bell’s theorem by constructing a ...
16
votes
6answers
3k views

What is Quantization?

In classical mechanics you construct an action (involving a Lagrangian in arbitrary generalized coordinates, a Hamiltonian in canonical coordinates [to make your EOM more "convenient & symmetric"])...

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