QUANTUM PHYSICS LECTURE 5 OPERATOR AND SCHRODINGERS EQUATION

QUANTUM PHYSICS LECTURE 5: OPERATOR AND SCHRODINGER’S EQUATION IKSAN BUKHORI M. PHIL.

POSTULATE OF QUANTUM MECHANICS

POSTULATE OF QUANTUM MECHANICS 4. A wave function which has definite position will typically have uncertain wavelength 5. A wave function which has definite wavelength will typically have uncertain position

POSTULATE OF QUANTUM MECHANICS

MOMENTUM OPERATOR Why? Ex:

GENERALIZING OPERATOR Operator: Something that operates on and changes (mathematical) object Simplest Example Object : Vector Operator : Matrix In quantum Physics Object : Complex Function Operator : Something that acts on complex function

LINEAR OPERATOR Examples: 1. Linear 2. Linear 3. Not Linear 4. Not Linear

COMMUTATOR Like matrix multiplication, the order of operator matters. While To measure the importance of order of operator, there is a quantity called commutator defined as For example,

EIGENVALUES AND EIGENFUNCTIONS

BACK TO POSTULATE OF QM To every observable quantity, there exists an operator associated with it. For example, momentum operator is given by Position operator is given by And energy operator is given by For every operator, the general form of the expectation value of the corresponding observable is given by and

THE COLLAPSE OF WAVE FUNCTION

THE COLLAPSE OF WAVE FUNCTION

COLLAPSE OF WAVE FUNCTION

SCHRODINGER EQUATION It describes how wave function evolves over time Where

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