A Computational Revisit of the Variational Principle: Estimating Ground State Energies of the 1D Harmonic Oscillator via Python

2025-06-05T21:34:33+07:00

Purpose of the study:To estimate the ground state energy of the one-dimensional harmonic oscillator using the variational principle and Python-based numerical methods.

Methodology:Python 3.11 was used with NumPy, SciPy, and Matplotlib libraries. The variational method was applied using multiple trial wavefunctions. Integrals were computed via Simpson’s rule, and optimization was done through parameter scanning.

Main Findings:The Gaussian trial wavefunction produced a ground state energy of 0.5003 ℏω, showing 0.06% error. Other trial functions were less accurate. The results confirm that the choice of trial function critically affects the energy estimate, and Python effectively supports variational computations in quantum systems.

Novelty/Originality of this study:This study integrates computational tools with the variational principle, presenting an accessible approach to energy estimation in quantum mechanics. It demonstrates how Python can facilitate variational analysis, making the method replicable and educationally useful for students and researchers.

Development of Online Learning Management in Physics Learning Technology Course

2025-06-07T14:44:36+07:00

Purpose of the study: Development of online learning management in Physics Learning Technology course.

Methodology: The research method used is the development research method with the research subjects of students of the Department of Physics Education, Faculty of Teacher Training and Education, Sebelas Maret University, Surakarta, Indonesia. Data were collected using an open questionnaire method and analyzed using a method of concluding from the opinions expressed by students participating in the course.

Main Findings: The development of an online learning management model for the Physics Learning Technology course in the Physics Education Study Program at Sebelas Maret University was carried out through the stages of planning, organizing, implementing, and supervising to achieve learning objectives. Planning involved preparing a blended learning-based course syllabus. Organizing included arranging the necessary materials, media, and learning tools. Implementation followed the planning and organizing stages, while supervision was conducted by analyzing student responses. The results show that all seven learning objectives were achieved, including the ability to collaborate, manage time, use online learning applications, select appropriate materials, complete assignments on time, rewrite information from library sources, and properly cite references.

Novelty/Originality of this study: Online learning management of Physics Learning Technology course can be done by learning of designing, organizing, actuating, and controlling according to learning objectives.

Schrödinger: Journal of Physics Education

A Computational Revisit of the Variational Principle: Estimating Ground State Energies of the 1D Harmonic Oscillator via Python

Development of Online Learning Management in Physics Learning Technology Course