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quantum.cmptr
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What is a quantum state of a system? I keep hearing it, but I'm not able to fully understand what it means, especially in relation to Bose-Einstein Condensate, and the Pauli Exclusion Principle.
What exactly is a quantum state?
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In summary, a quantum state of a system is a mathematical object that describes all observable properties of the system. In classical physics, it is represented by a point in phase space, while in quantum mechanics, it is represented by a vector in a Hilbert space. This concept is important in understanding Bose-Einstein Condensate and the Pauli Exclusion Principle. However, the technical details of this concept may be too advanced for someone in 7th grade to fully grasp.
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samalkhaiat
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Do you know what a classical state of a system is?quantum.cmptr said:
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quantum.cmptr
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No, I do not.
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samalkhaiat
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In general, the state of physical system is a mathematical object(s) in terms of which all observable properties of the system can be calculated. In classical physics the state of the system is a point in phase space; the coordinates and the corresponding momenta. In quantum mechanics, the state of the system is a vector in an abstract vector space called the Hilbert space. In general, given the state of the physical system at some initial time, the equations of the theory tell you what the state will look like in a later time.quantum.cmptr said:
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Technically, in most axiomatizations, a state is a (unit) ray, not a vector. But this mathematical subtlety is far beyond our OP's current level of understanding, as I suspect he's not even started his university studies, whatever the subject.
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quantum.cmptr
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I'm not even in high school (7th grade).
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samalkhaiat
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Are you "nitpicking" on me?dextercioby said:
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quantum.cmptr
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Uh...
Related to What exactly is a quantum state?
What is a quantum state?
A quantum state is a mathematical representation of the physical properties of a quantum system. It contains all the information about the system, such as its position, momentum, and energy, and can be used to predict the behavior and evolution of the system over time.
How is a quantum state different from a classical state?
A classical state describes the physical properties of a system using classical mechanics, which is based on Newton's laws of motion. A quantum state, on the other hand, describes the properties of a system using quantum mechanics, which takes into account the behavior of particles at the subatomic level.
What is the uncertainty principle and how does it relate to quantum states?
The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is because the act of measuring one property affects the other, making it impossible to determine both values simultaneously. This principle is a fundamental aspect of quantum mechanics and is related to the probabilistic nature of quantum states.
Can a quantum state be observed or measured directly?
No, a quantum state cannot be observed or measured directly. Instead, scientists use mathematical equations and models to describe and predict the behavior of quantum systems based on their quantum states. The act of measuring a quantum state can also alter its properties, making it impossible to observe directly.
Can a quantum state be changed or manipulated?
Yes, a quantum state can be changed or manipulated through a process known as quantum control. This involves using external forces, such as electric or magnetic fields, to alter the properties of a quantum system and thereby change its quantum state. This is a crucial aspect of quantum computing, where the manipulation of quantum states allows for the processing of information in a fundamentally different way than classical computers.
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