Probability amplitude versus probability distribution

In summary, the discussion is about the physical implications of two probability distributions being equal to each other even though their probability amplitudes are not the same. The probability amplitude represents the likelihood of a particle existing at a certain position, while the probability distribution shows the overall probability of the particle's position. This means that the probability amplitude encodes information about the direction of the wavefunction, while the probability distribution only gives a snapshot of the particle's position.
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Homework Statement


The question is "Comment on the physical consequence of two probability distributions being equal to each other even though the probability amplitudes are not the same."


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The Attempt at a Solution


I understand that the modulus squared of the probability amplitude is the probability density which shows the probability of a particle existing at a certain position, but I guess I don't fully understand what the probability amplitude is then. If both particles have the same probability distribution, then they would have the same likelihood of existing in the same position, correct? But what about different prob amps?
 
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  • #2
Knowing the probability distribution is rather like having a photograph of a train. The photograph tells you exactly where the train is, but not which way it's moving. Information about which way the wavefunction is moving is encoded in the amplitude.
 

FAQ: Probability amplitude versus probability distribution

1. What is the difference between probability amplitude and probability distribution?

Probability amplitude is a complex number that represents the likelihood of a quantum system being in a particular state. It is a fundamental concept in quantum mechanics and is used to calculate the probability of a measurement outcome. Probability distribution, on the other hand, is a function that describes the probability of a measurement outcome occurring in a classical system. It is a more intuitive concept that is widely used in classical probability theory.

2. How are probability amplitude and probability distribution related?

Probability amplitude and probability distribution are related through the Born rule, which states that the square of the amplitude is equal to the probability of measuring a particular state. In other words, the probability distribution can be obtained by taking the square of the absolute value of the probability amplitude.

3. Can probability amplitude be negative?

Yes, probability amplitude can be negative. In quantum mechanics, probability amplitude is a complex number that contains both magnitude and phase information. The negative sign of the amplitude represents the interference between different states, which is a fundamental concept in quantum mechanics.

4. How is probability amplitude calculated?

Probability amplitude is calculated using the Schrödinger equation and the Hamiltonian operator, which describe the evolution of a quantum system. The amplitude is obtained by solving the equation and finding the coefficients of the different states in the system.

5. What is the physical significance of probability amplitude?

Probability amplitude is a fundamental concept in quantum mechanics that helps to explain the probabilistic nature of the quantum world. It represents the chance of a quantum system being in a specific state and is used to calculate the probability of a measurement outcome. It is a crucial concept in understanding the behavior of particles at the microscopic level and has led to many important discoveries in modern physics.

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