Understanding Direct Product States in Linear Algebra

In summary, multiple quantum particles are a group of particles that exhibit quantum behavior, such as being able to exist in multiple states simultaneously. They behave differently from classical particles in that they can also become entangled and influence each other over large distances. In the field of quantum computing, multiple quantum particles are essential for creating qubits, which have the potential to store and process more information than classical bits. These particles are studied and manipulated in the laboratory using various techniques, and their potential applications include quantum computing, cryptography, precision measurement, sensors, and new materials and technologies.
  • #1
homology
306
1
So why is it that if you have a system with two distinguisable particles why is their state vector written as

|psi>=|psi_1>|psi_2>

what's this product? Is this product still "in" the original hilbert space?

Kevin
 
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  • #2
I think the state is in the tensor product of the particle spaces.
 
  • #3
Huh, is that so, I'll have to play around with that idea and see where it takes me. Thanks SelfAdjoint.

Kevin
 
  • #4
The state |a>|b> is also called a "direct product state", and this basic idea is discussed in most books on linear algebra.
Regards,
Reilly Atkinson
 

1. What are multiple quantum particles?

Multiple quantum particles refer to a group of particles that exhibit quantum behavior, meaning they can exist in multiple states or positions simultaneously. Examples of multiple quantum particles include photons, electrons, and atoms.

2. How do multiple quantum particles behave differently from classical particles?

Unlike classical particles, multiple quantum particles can exist in multiple states or positions at the same time, known as superposition. They also have the ability to become entangled with one another, meaning their states are connected and can influence each other, even over large distances.

3. What is the significance of multiple quantum particles in quantum computing?

Multiple quantum particles play a crucial role in quantum computing, as their ability to exist in multiple states allows for the creation of quantum bits or qubits. Qubits have the potential to store and process significantly more information compared to classical bits, making them essential for the development of powerful quantum computers.

4. How are multiple quantum particles studied and manipulated in the laboratory?

Multiple quantum particles are studied and manipulated using various techniques, such as laser cooling and trapping, magnetic fields, and electron microscopy. These methods allow scientists to control and observe the behavior of multiple quantum particles to further understand their properties and potential applications.

5. What are some potential applications of multiple quantum particles?

Multiple quantum particles have potential applications in various fields, including quantum computing, cryptography, and precision measurement. They can also be used in sensors and metrology devices, as well as in the development of new materials and technologies.

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