Can quantum mechanics without complex numbers?

Can quantum mechanics without complex numbers?

Quantum Mechanics without Complex Numbers: A Simple Model for the Electron Wavefunction Including Spin. The mapping of the real two-dimensional vector phasor to the complex plane permits this to satisfy the standard time-dependent Schroedinger equation.

Why do we need complex numbers for quantum mechanics?

It is particularly helpful to use complex numbers to model periodic phenomena, especially to operate with phase differences. Mathematically, one can treat a physical quantity as being complex, but address physical meaning only to its real part.

Does quantum mechanics require complex analysis?

The spectrum condition is also fundamentally important: it ensures the existence of a vacuum state, which in turn is the basis for the definition of “particle” in quantum field theory. So yes, complex analysis is important in quantum mechanics, even if this isn’t evident early in the curriculum.

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What does quantum mechanics require?

Quantum mechanics is an important tool to understand at the theoretical level the electronic structure of chemical compounds and the mechanism, thermodynamics, and kinetics of chemical reactions.

Are complex numbers necessary?

Complex numbers, i.e., numbers with a real and an imaginary part, are essential for mathematical analysis, while their role in other subjects, such as electromagnetism or special relativity, is far less fundamental.

Can probability be a complex number?

According to the author of various papers on exotic probability, Saul Youssef, the valid possible alternatives for probability values are the real numbers, the complex numbers and the quaternions.

Do I need complex analysis?

Complex Analysis is rarely a requirement for completing the mathematics major. It is more often an elective or perhaps a required course within a particular sub-track of the major. The course is also very useful for students planning to go to graduate school in mathematics or applied mathematics.

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Does physics use complex analysis?

Complex numbers and complex analysis show up everywhere in mathematics and physics. Algebraically, complex numbers are closed. This is a good algebraic property for a field. They’ve been studied in mathematics since the 17th century because of their applications to mathematics, mechanics, waves, etc.

Why are complex solutions important?

Answer: it is important to learn about complex solution because polynomial equation formed over a complex number can only be solved by a complex number. this is so because, the fundamental theorem of algebra state that every polynomial equation in one variable with complex coefficient has at least one complex solution.

Why are complex numbers needed In quantum mechanics?

Some answers for the introductory level: American Journal of Physics: Vol 88, No 1 Why are complex numbers needed in quantum mechanics? Some answers for the introductory level more… Complex numbers are broadly used in physics, normally as a calculation tool that makes things easier due to Euler’s formula.

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Does the imaginary unit I appear explicitly in quantum mechanics?

However, the situation seems to be different in quantum mechanics, since the imaginary unit i appears explicitly in its fundamental equations. From a learning perspective, this can create some challenges to newcomers.

Is Stueckelberg’s theory of quantum mechanics real?

Among them, the work of Stueckelberg (Ref. 7) stands out as a plausible formulation of quantum mechanics in real Hilbert space (see Ref. 8 for a pedagogical introduction).

How do you find the real part of a complex quantity?

The usual method of getting the real part of a complex quantity, by taking half the sum of the quantity itself and its conjugate, cannot be applied since a bra and a ket vector are of different natures and cannot be added.” 5.