Shrodinger Equation Help: Solving for Wavefunction and Energy in a 1D Box

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In summary, the conversation discusses a particle of mass m being confined in a 1 dimensional box and the potential energy associated with it. The task is to write the Schrodinger equation for both inside and outside of the box, solve it for the inside of the box in the form of a wavefunction, and determine possible values of C and conditions for the constants A and B in order for the wavefunction to be a satisfactory solution. Additionally, the energy is to be expressed in terms of C. The conversation also mentions using Euler's rules and asks for clarification on determining possible values of C.
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shrugBERT
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Homework Statement


A particle of mass m in confined in a 1 dimensional box with origin at the center. the box extends from -a/2 to a/2 the potential energy is v(x) = 0 where -a/2<x< a/2 and infinite when x > a/2.

I have to write the shrodinger equation for the outside and inside of the box, solve the equation for inside the box in the form of wavefunc = A sin (cx) + B cos (cx). Give a rule determining all possible values of C and for each possible c determined give the conditions the constants A and B must adhere to to make the wavefunction a satisfactory solution to the shrodinger EQ

and last but not least express the energy in terms of C.

Homework Equations



H psi = E psi
h bar (used down below) = h/2pi
edit: oh i also used L instead of a for a variable when talking about the length of the box

The Attempt at a Solution



S.E. for particle outside box

psi(x) = sqrt(2/L) sin (n pi x)/L

S.E. for particle inside box

(-h bar^2)/2m + d psi/dx^2 = i(h bar) d psi/dtsolution to S.E for particle inside a box

Psi (x,t) = Ae^(i2pi/lamda - omega t) ==== Ae^(ikx - iwt)

====
solution using Eulers' rules
Acos(kx - wt) + iAsin (kx-wt)are these answers right for above questions? or do the answers have to be more specific, i don't know I am new to all this.

ok when they ask to give a rule that determines all possible values of c what does that mean? this might seem dumb but I am not even sure what c is.i registered for this forum specifically because I am having a lot of trouble in biophysical chem class, if anyone wants to help me it would be great.
 
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ooh and i can post any work leading up to the answers in the answer section but I refrained because I'm pretty sure my notation is horrible.
 

What is the Schrodinger Equation?

The Schrodinger Equation is a fundamental equation in quantum mechanics that describes how the state of a physical system changes over time. It is used to predict the behavior of particles at the atomic and subatomic level.

Who was Erwin Schrodinger and why is the equation named after him?

Erwin Schrodinger was an Austrian physicist who developed the Schrodinger Equation in 1925. The equation is named after him because he was the first to propose it as a way to describe the behavior of quantum particles.

What is the difference between the time-dependent and time-independent versions of the Schrodinger Equation?

The time-dependent Schrodinger Equation describes how the state of a system changes over time, while the time-independent Schrodinger Equation describes the stationary states of a system, which do not change over time. The time-independent version is used to solve for the energy levels and wave functions of a quantum system.

What are the physical meanings of the terms in the Schrodinger Equation?

The term "i ħ ∂/∂t" represents the time evolution of the wave function, "Ĥ" represents the total energy of the system, "Ψ" is the wave function of the system, and "V" is the potential energy of the system. The equation describes how the wave function changes over time in response to the energy and potential of the system.

How is the Schrodinger Equation used in real-world applications?

The Schrodinger Equation is used in many areas of physics, including quantum mechanics, solid state physics, and nuclear physics. It is used to study the behavior of particles at the atomic and subatomic level, and has applications in fields such as chemistry, materials science, and electronics. It is also used in the development of new technologies, such as quantum computers and medical imaging techniques.

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