Exploring the Fundamentals of Quantum Mechanics: Unraveling Common Doubts

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In summary, the conversation discusses doubts about basic quantum mechanics, specifically the differences between the ordinary wave equation and Schrodinger equation, the dimension and measurability of the wavefunction, and the continuity of ψ and ∂ψ/∂x. The book suggests that the Schrodinger equation is designed to make the wave function independent of particle properties, but the speaker has difficulty understanding this. They also raise the question of how the measurement process in quantum mechanics affects the measurability of the wavefunction. Finally, they consider the relationship between ψ and ∂ψ/∂x, noting that while ψ must be continuous, it does not necessarily follow that ∂ψ/∂x must also
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Homework Statement



I've some doubts in the basic quantum mechanics.I know these are too simple. But can't figure out the exact answer.


1. Ordinary wave equation relates second order time derivative to second order space derivative.But Schrodinger equation connects first order time derivative with second order space derivative.Why this difference?

2. I've seen in a book that wavefunction should have a dimension of L-3/2(because |ψ|2dx should be dimensionless).Then why can't we measure wavefunction?

3.From Schrodinger equation, ψ should be continuous.But how can we say that ∂ψ/∂x should be continuous also?


The Attempt at a Solution



1. A book says this is to make wave function independant of the properties of the particle(if wave function for free particle is considered).But i can't understand it properly.

3.I think (may be wrong) when ψ is a continuous function of x, ∂ψ/∂t should be a continuos function of x. ie, LHS of Sch. equation is continous. Then RHS also need to be continuous. But it don't imply that ∂ψ/∂x should be continuous.
 
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In regards to 2, think about what happens when you measure something in quantum mechanics, how would this make it hard for you to measure the wavefunction?
 

FAQ: Exploring the Fundamentals of Quantum Mechanics: Unraveling Common Doubts

What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It explains how these particles interact and behave, and has led to many technological advancements such as computers and lasers.

What is the uncertainty principle?

The uncertainty principle states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This is due to the probabilistic nature of quantum mechanics, where we can only predict the likelihood of a particle's position or momentum at any given time.

What is quantum superposition?

Quantum superposition is the ability of a quantum system to exist in multiple states at the same time. This means that a particle can be in two or more places, or have two or more properties, simultaneously. It is a fundamental principle of quantum mechanics and has been demonstrated in experiments such as the double-slit experiment.

What is entanglement?

Entanglement is a phenomenon in which two or more particles become connected in such a way that the state of one particle is dependent on the state of the other, even if they are separated by large distances. This has been described as "spooky action at a distance" by Einstein, and has been proven through various experiments.

How does quantum mechanics relate to everyday life?

Quantum mechanics may seem like an abstract and complex theory, but it has many practical applications in our everyday lives. For example, it is used in technologies such as transistors in electronic devices, GPS technology, and medical imaging. It also plays a crucial role in understanding chemical reactions and the behavior of materials at the atomic level.

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